← Ten hundreds make one thousand · Place-Value Regrouping

Ten hundreds make one thousand · 12 practice problems

2.MD.C.8

Generated variants — 12

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy answer: $81

Sophie has 8 ten-dollar bills and 10 dimes. How much money does Sophie have in all?

Show solution
1 · Understandwhat's really being asked

Sophie has 8 ten-dollar bills and 10 dimes. Find the total amount of money.

Givens
  • There are 8 ten-dollar bills.
  • There are 10 dimes (each dime is 10 cents).
  • Ten dimes make one dollar.
Unknowns
  • The total amount of money in all.
Constraints
  • Money is counted in dollars and cents; 100 cents make a dollar.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

There are two kinds of money, so I find the value of each group separately by tracking its units (bills to dollars, dimes to dollars) and then add the two totals.

3 · Execute3 carry out the plan

1Value of the ten-dollar bills

#7 Identify Subproblems 2.MD.C.8
Each ten-dollar bill is worth 10,andthereare8ofthem,sothebillsareworth8times10, and there are 8 of them, so the bills are worth 8 times10, which is $80.
8×$10=$808 \times \$10 = \$80
Counting by tens gives the dollar value of the bills.

2Value of the dimes

#8 Analyze the Units 2.MD.C.8
Each dime is 10 cents, and ten dimes make one dollar. So 10 dimes are 100 cents, which is $1.
10×10 cents=100 cents=$110 \times 10\text{ cents} = 100\text{ cents} = \$1
Because ten dimes equal a dollar, the dimes bundle into whole dollars, the same way ten hundreds make a thousand.

3Add the two amounts

#7 Identify Subproblems 2.MD.C.8
Combine the bills and the dimes: 80fromthebillsplus80 from the bills plus1 from the dimes is $81.
$80+$1=$81\$80 + \$1 = \$81
The total money is just the dollar amounts of each group added together.
Answer: $81
4 · Reviewdoes it hold up?

The bills alone are 80andthedimesadd80 and the dimes add1, so a total of 81issensible;100centsisexactly81 is sensible; 100 cents is exactly1, confirming $81.

Another way: Convert everything to cents: 8 bills = 8000 cents, 10 dimes = 100 cents, total 8100 cents = $81.

Standardsmin grade 2
  • 2.MD.C.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies — Finding and adding the values of ten-dollar bills and dimes.
💡Takeaway. Ten dimes bundle up into a dollar, so a pile of dimes is just a few dollars to add to your bills!
Variant 2 easy answer: $51

Sophie has 5 ten-dollar bills and 10 dimes. How much money does Sophie have in all?

Show solution
1 · Understandwhat's really being asked

Sophie has 5 ten-dollar bills and 10 dimes. Find the total amount of money.

Givens
  • There are 5 ten-dollar bills.
  • There are 10 dimes (each dime is 10 cents).
  • Ten dimes make one dollar.
Unknowns
  • The total amount of money in all.
Constraints
  • Money is counted in dollars and cents; 100 cents make a dollar.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

There are two kinds of money, so I find the value of each group separately by tracking its units (bills to dollars, dimes to dollars) and then add the two totals.

3 · Execute3 carry out the plan

1Value of the ten-dollar bills

#7 Identify Subproblems 2.MD.C.8
Each ten-dollar bill is worth 10,andthereare5ofthem,sothebillsareworth5times10, and there are 5 of them, so the bills are worth 5 times10, which is $50.
5×$10=$505 \times \$10 = \$50
Counting by tens gives the dollar value of the bills.

2Value of the dimes

#8 Analyze the Units 2.MD.C.8
Each dime is 10 cents, and ten dimes make one dollar. So 10 dimes are 100 cents, which is $1.
10×10 cents=100 cents=$110 \times 10\text{ cents} = 100\text{ cents} = \$1
Because ten dimes equal a dollar, the dimes bundle into whole dollars, the same way ten hundreds make a thousand.

3Add the two amounts

#7 Identify Subproblems 2.MD.C.8
Combine the bills and the dimes: 50fromthebillsplus50 from the bills plus1 from the dimes is $51.
$50+$1=$51\$50 + \$1 = \$51
The total money is just the dollar amounts of each group added together.
Answer: $51
4 · Reviewdoes it hold up?

The bills alone are 50andthedimesadd50 and the dimes add1, so a total of 51issensible;100centsisexactly51 is sensible; 100 cents is exactly1, confirming $51.

Another way: Convert everything to cents: 5 bills = 5000 cents, 10 dimes = 100 cents, total 5100 cents = $51.

Standardsmin grade 2
  • 2.MD.C.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies — Finding and adding the values of ten-dollar bills and dimes.
💡Takeaway. Ten dimes bundle up into a dollar, so a pile of dimes is just a few dollars to add to your bills!
Variant 3 easy answer: $32

Sophie has 3 ten-dollar bills and 20 dimes. How much money does Sophie have in all?

Show solution
1 · Understandwhat's really being asked

Sophie has 3 ten-dollar bills and 20 dimes. Find the total amount of money.

Givens
  • There are 3 ten-dollar bills.
  • There are 20 dimes (each dime is 10 cents).
  • Ten dimes make one dollar.
Unknowns
  • The total amount of money in all.
Constraints
  • Money is counted in dollars and cents; 100 cents make a dollar.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

There are two kinds of money, so I find the value of each group separately by tracking its units (bills to dollars, dimes to dollars) and then add the two totals.

3 · Execute3 carry out the plan

1Value of the ten-dollar bills

#7 Identify Subproblems 2.MD.C.8
Each ten-dollar bill is worth 10,andthereare3ofthem,sothebillsareworth3times10, and there are 3 of them, so the bills are worth 3 times10, which is $30.
3×$10=$303 \times \$10 = \$30
Counting by tens gives the dollar value of the bills.

2Value of the dimes

#8 Analyze the Units 2.MD.C.8
Each dime is 10 cents, and ten dimes make one dollar. So 20 dimes are 200 cents, which is $2.
20×10 cents=200 cents=$220 \times 10\text{ cents} = 200\text{ cents} = \$2
Because ten dimes equal a dollar, the dimes bundle into whole dollars, the same way ten hundreds make a thousand.

3Add the two amounts

#7 Identify Subproblems 2.MD.C.8
Combine the bills and the dimes: 30fromthebillsplus30 from the bills plus2 from the dimes is $32.
$30+$2=$32\$30 + \$2 = \$32
The total money is just the dollar amounts of each group added together.
Answer: $32
4 · Reviewdoes it hold up?

The bills alone are 30andthedimesadd30 and the dimes add2, so a total of 32issensible;200centsisexactly32 is sensible; 200 cents is exactly2, confirming $32.

Another way: Convert everything to cents: 3 bills = 3000 cents, 20 dimes = 200 cents, total 3200 cents = $32.

Standardsmin grade 2
  • 2.MD.C.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies — Finding and adding the values of ten-dollar bills and dimes.
💡Takeaway. Ten dimes bundle up into a dollar, so a pile of dimes is just a few dollars to add to your bills!
Variant 4 easy answer: $62

Sophie has 6 ten-dollar bills and 20 dimes. How much money does Sophie have in all?

Show solution
1 · Understandwhat's really being asked

Sophie has 6 ten-dollar bills and 20 dimes. Find the total amount of money.

Givens
  • There are 6 ten-dollar bills.
  • There are 20 dimes (each dime is 10 cents).
  • Ten dimes make one dollar.
Unknowns
  • The total amount of money in all.
Constraints
  • Money is counted in dollars and cents; 100 cents make a dollar.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

There are two kinds of money, so I find the value of each group separately by tracking its units (bills to dollars, dimes to dollars) and then add the two totals.

3 · Execute3 carry out the plan

1Value of the ten-dollar bills

#7 Identify Subproblems 2.MD.C.8
Each ten-dollar bill is worth 10,andthereare6ofthem,sothebillsareworth6times10, and there are 6 of them, so the bills are worth 6 times10, which is $60.
6×$10=$606 \times \$10 = \$60
Counting by tens gives the dollar value of the bills.

2Value of the dimes

#8 Analyze the Units 2.MD.C.8
Each dime is 10 cents, and ten dimes make one dollar. So 20 dimes are 200 cents, which is $2.
20×10 cents=200 cents=$220 \times 10\text{ cents} = 200\text{ cents} = \$2
Because ten dimes equal a dollar, the dimes bundle into whole dollars, the same way ten hundreds make a thousand.

3Add the two amounts

#7 Identify Subproblems 2.MD.C.8
Combine the bills and the dimes: 60fromthebillsplus60 from the bills plus2 from the dimes is $62.
$60+$2=$62\$60 + \$2 = \$62
The total money is just the dollar amounts of each group added together.
Answer: $62
4 · Reviewdoes it hold up?

The bills alone are 60andthedimesadd60 and the dimes add2, so a total of 62issensible;200centsisexactly62 is sensible; 200 cents is exactly2, confirming $62.

Another way: Convert everything to cents: 6 bills = 6000 cents, 20 dimes = 200 cents, total 6200 cents = $62.

Standardsmin grade 2
  • 2.MD.C.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies — Finding and adding the values of ten-dollar bills and dimes.
💡Takeaway. Ten dimes bundle up into a dollar, so a pile of dimes is just a few dollars to add to your bills!
Variant 5 medium answer: $73

Sophie has 7 ten-dollar bills and 30 dimes. How much money does Sophie have in all?

Show solution
1 · Understandwhat's really being asked

Sophie has 7 ten-dollar bills and 30 dimes. Find the total amount of money.

Givens
  • There are 7 ten-dollar bills.
  • There are 30 dimes (each dime is 10 cents).
  • Ten dimes make one dollar.
Unknowns
  • The total amount of money in all.
Constraints
  • Money is counted in dollars and cents; 100 cents make a dollar.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

There are two kinds of money, so I find the value of each group separately by tracking its units (bills to dollars, dimes to dollars) and then add the two totals.

3 · Execute3 carry out the plan

1Value of the ten-dollar bills

#7 Identify Subproblems 2.MD.C.8
Each ten-dollar bill is worth 10,andthereare7ofthem,sothebillsareworth7times10, and there are 7 of them, so the bills are worth 7 times10, which is $70.
7×$10=$707 \times \$10 = \$70
Counting by tens gives the dollar value of the bills.

2Value of the dimes

#8 Analyze the Units 2.MD.C.8
Each dime is 10 cents, and ten dimes make one dollar. So 30 dimes are 300 cents, which is $3.
30×10 cents=300 cents=$330 \times 10\text{ cents} = 300\text{ cents} = \$3
Because ten dimes equal a dollar, the dimes bundle into whole dollars, the same way ten hundreds make a thousand.

3Add the two amounts

#7 Identify Subproblems 2.MD.C.8
Combine the bills and the dimes: 70fromthebillsplus70 from the bills plus3 from the dimes is $73.
$70+$3=$73\$70 + \$3 = \$73
The total money is just the dollar amounts of each group added together.
Answer: $73
4 · Reviewdoes it hold up?

The bills alone are 70andthedimesadd70 and the dimes add3, so a total of 73issensible;300centsisexactly73 is sensible; 300 cents is exactly3, confirming $73.

Another way: Convert everything to cents: 7 bills = 7000 cents, 30 dimes = 300 cents, total 7300 cents = $73.

Standardsmin grade 2
  • 2.MD.C.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies — Finding and adding the values of ten-dollar bills and dimes.
💡Takeaway. Ten dimes bundle up into a dollar, so a pile of dimes is just a few dollars to add to your bills!
Variant 6 medium answer: $23

Sophie has 2 ten-dollar bills and 30 dimes. How much money does Sophie have in all?

Show solution
1 · Understandwhat's really being asked

Sophie has 2 ten-dollar bills and 30 dimes. Find the total amount of money.

Givens
  • There are 2 ten-dollar bills.
  • There are 30 dimes (each dime is 10 cents).
  • Ten dimes make one dollar.
Unknowns
  • The total amount of money in all.
Constraints
  • Money is counted in dollars and cents; 100 cents make a dollar.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

There are two kinds of money, so I find the value of each group separately by tracking its units (bills to dollars, dimes to dollars) and then add the two totals.

3 · Execute3 carry out the plan

1Value of the ten-dollar bills

#7 Identify Subproblems 2.MD.C.8
Each ten-dollar bill is worth 10,andthereare2ofthem,sothebillsareworth2times10, and there are 2 of them, so the bills are worth 2 times10, which is $20.
2×$10=$202 \times \$10 = \$20
Counting by tens gives the dollar value of the bills.

2Value of the dimes

#8 Analyze the Units 2.MD.C.8
Each dime is 10 cents, and ten dimes make one dollar. So 30 dimes are 300 cents, which is $3.
30×10 cents=300 cents=$330 \times 10\text{ cents} = 300\text{ cents} = \$3
Because ten dimes equal a dollar, the dimes bundle into whole dollars, the same way ten hundreds make a thousand.

3Add the two amounts

#7 Identify Subproblems 2.MD.C.8
Combine the bills and the dimes: 20fromthebillsplus20 from the bills plus3 from the dimes is $23.
$20+$3=$23\$20 + \$3 = \$23
The total money is just the dollar amounts of each group added together.
Answer: $23
4 · Reviewdoes it hold up?

The bills alone are 20andthedimesadd20 and the dimes add3, so a total of 23issensible;300centsisexactly23 is sensible; 300 cents is exactly3, confirming $23.

Another way: Convert everything to cents: 2 bills = 2000 cents, 30 dimes = 300 cents, total 2300 cents = $23.

Standardsmin grade 2
  • 2.MD.C.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies — Finding and adding the values of ten-dollar bills and dimes.
💡Takeaway. Ten dimes bundle up into a dollar, so a pile of dimes is just a few dollars to add to your bills!
Variant 7 medium answer: $44

Sophie has 4 ten-dollar bills and 40 dimes. How much money does Sophie have in all?

Show solution
1 · Understandwhat's really being asked

Sophie has 4 ten-dollar bills and 40 dimes. Find the total amount of money.

Givens
  • There are 4 ten-dollar bills.
  • There are 40 dimes (each dime is 10 cents).
  • Ten dimes make one dollar.
Unknowns
  • The total amount of money in all.
Constraints
  • Money is counted in dollars and cents; 100 cents make a dollar.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

There are two kinds of money, so I find the value of each group separately by tracking its units (bills to dollars, dimes to dollars) and then add the two totals.

3 · Execute3 carry out the plan

1Value of the ten-dollar bills

#7 Identify Subproblems 2.MD.C.8
Each ten-dollar bill is worth 10,andthereare4ofthem,sothebillsareworth4times10, and there are 4 of them, so the bills are worth 4 times10, which is $40.
4×$10=$404 \times \$10 = \$40
Counting by tens gives the dollar value of the bills.

2Value of the dimes

#8 Analyze the Units 2.MD.C.8
Each dime is 10 cents, and ten dimes make one dollar. So 40 dimes are 400 cents, which is $4.
40×10 cents=400 cents=$440 \times 10\text{ cents} = 400\text{ cents} = \$4
Because ten dimes equal a dollar, the dimes bundle into whole dollars, the same way ten hundreds make a thousand.

3Add the two amounts

#7 Identify Subproblems 2.MD.C.8
Combine the bills and the dimes: 40fromthebillsplus40 from the bills plus4 from the dimes is $44.
$40+$4=$44\$40 + \$4 = \$44
The total money is just the dollar amounts of each group added together.
Answer: $44
4 · Reviewdoes it hold up?

The bills alone are 40andthedimesadd40 and the dimes add4, so a total of 44issensible;400centsisexactly44 is sensible; 400 cents is exactly4, confirming $44.

Another way: Convert everything to cents: 4 bills = 4000 cents, 40 dimes = 400 cents, total 4400 cents = $44.

Standardsmin grade 2
  • 2.MD.C.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies — Finding and adding the values of ten-dollar bills and dimes.
💡Takeaway. Ten dimes bundle up into a dollar, so a pile of dimes is just a few dollars to add to your bills!
Variant 8 medium answer: $15

Sophie has 1 ten-dollar bills and 50 dimes. How much money does Sophie have in all?

Show solution
1 · Understandwhat's really being asked

Sophie has 1 ten-dollar bills and 50 dimes. Find the total amount of money.

Givens
  • There are 1 ten-dollar bills.
  • There are 50 dimes (each dime is 10 cents).
  • Ten dimes make one dollar.
Unknowns
  • The total amount of money in all.
Constraints
  • Money is counted in dollars and cents; 100 cents make a dollar.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

There are two kinds of money, so I find the value of each group separately by tracking its units (bills to dollars, dimes to dollars) and then add the two totals.

3 · Execute3 carry out the plan

1Value of the ten-dollar bills

#7 Identify Subproblems 2.MD.C.8
Each ten-dollar bill is worth 10,andthereare1ofthem,sothebillsareworth1times10, and there are 1 of them, so the bills are worth 1 times10, which is $10.
1×$10=$101 \times \$10 = \$10
Counting by tens gives the dollar value of the bills.

2Value of the dimes

#8 Analyze the Units 2.MD.C.8
Each dime is 10 cents, and ten dimes make one dollar. So 50 dimes are 500 cents, which is $5.
50×10 cents=500 cents=$550 \times 10\text{ cents} = 500\text{ cents} = \$5
Because ten dimes equal a dollar, the dimes bundle into whole dollars, the same way ten hundreds make a thousand.

3Add the two amounts

#7 Identify Subproblems 2.MD.C.8
Combine the bills and the dimes: 10fromthebillsplus10 from the bills plus5 from the dimes is $15.
$10+$5=$15\$10 + \$5 = \$15
The total money is just the dollar amounts of each group added together.
Answer: $15
4 · Reviewdoes it hold up?

The bills alone are 10andthedimesadd10 and the dimes add5, so a total of 15issensible;500centsisexactly15 is sensible; 500 cents is exactly5, confirming $15.

Another way: Convert everything to cents: 1 bills = 1000 cents, 50 dimes = 500 cents, total 1500 cents = $15.

Standardsmin grade 2
  • 2.MD.C.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies — Finding and adding the values of ten-dollar bills and dimes.
💡Takeaway. Ten dimes bundle up into a dollar, so a pile of dimes is just a few dollars to add to your bills!
Variant 9 hard answer: $55

Sophie has 5 ten-dollar bills and 50 dimes. How much money does Sophie have in all?

Show solution
1 · Understandwhat's really being asked

Sophie has 5 ten-dollar bills and 50 dimes. Find the total amount of money.

Givens
  • There are 5 ten-dollar bills.
  • There are 50 dimes (each dime is 10 cents).
  • Ten dimes make one dollar.
Unknowns
  • The total amount of money in all.
Constraints
  • Money is counted in dollars and cents; 100 cents make a dollar.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

There are two kinds of money, so I find the value of each group separately by tracking its units (bills to dollars, dimes to dollars) and then add the two totals.

3 · Execute3 carry out the plan

1Value of the ten-dollar bills

#7 Identify Subproblems 2.MD.C.8
Each ten-dollar bill is worth 10,andthereare5ofthem,sothebillsareworth5times10, and there are 5 of them, so the bills are worth 5 times10, which is $50.
5×$10=$505 \times \$10 = \$50
Counting by tens gives the dollar value of the bills.

2Value of the dimes

#8 Analyze the Units 2.MD.C.8
Each dime is 10 cents, and ten dimes make one dollar. So 50 dimes are 500 cents, which is $5.
50×10 cents=500 cents=$550 \times 10\text{ cents} = 500\text{ cents} = \$5
Because ten dimes equal a dollar, the dimes bundle into whole dollars, the same way ten hundreds make a thousand.

3Add the two amounts

#7 Identify Subproblems 2.MD.C.8
Combine the bills and the dimes: 50fromthebillsplus50 from the bills plus5 from the dimes is $55.
$50+$5=$55\$50 + \$5 = \$55
The total money is just the dollar amounts of each group added together.
Answer: $55
4 · Reviewdoes it hold up?

The bills alone are 50andthedimesadd50 and the dimes add5, so a total of 55issensible;500centsisexactly55 is sensible; 500 cents is exactly5, confirming $55.

Another way: Convert everything to cents: 5 bills = 5000 cents, 50 dimes = 500 cents, total 5500 cents = $55.

Standardsmin grade 2
  • 2.MD.C.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies — Finding and adding the values of ten-dollar bills and dimes.
💡Takeaway. Ten dimes bundle up into a dollar, so a pile of dimes is just a few dollars to add to your bills!
Variant 10 hard answer: $36

Sophie has 3 ten-dollar bills and 60 dimes. How much money does Sophie have in all?

Show solution
1 · Understandwhat's really being asked

Sophie has 3 ten-dollar bills and 60 dimes. Find the total amount of money.

Givens
  • There are 3 ten-dollar bills.
  • There are 60 dimes (each dime is 10 cents).
  • Ten dimes make one dollar.
Unknowns
  • The total amount of money in all.
Constraints
  • Money is counted in dollars and cents; 100 cents make a dollar.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

There are two kinds of money, so I find the value of each group separately by tracking its units (bills to dollars, dimes to dollars) and then add the two totals.

3 · Execute3 carry out the plan

1Value of the ten-dollar bills

#7 Identify Subproblems 2.MD.C.8
Each ten-dollar bill is worth 10,andthereare3ofthem,sothebillsareworth3times10, and there are 3 of them, so the bills are worth 3 times10, which is $30.
3×$10=$303 \times \$10 = \$30
Counting by tens gives the dollar value of the bills.

2Value of the dimes

#8 Analyze the Units 2.MD.C.8
Each dime is 10 cents, and ten dimes make one dollar. So 60 dimes are 600 cents, which is $6.
60×10 cents=600 cents=$660 \times 10\text{ cents} = 600\text{ cents} = \$6
Because ten dimes equal a dollar, the dimes bundle into whole dollars, the same way ten hundreds make a thousand.

3Add the two amounts

#7 Identify Subproblems 2.MD.C.8
Combine the bills and the dimes: 30fromthebillsplus30 from the bills plus6 from the dimes is $36.
$30+$6=$36\$30 + \$6 = \$36
The total money is just the dollar amounts of each group added together.
Answer: $36
4 · Reviewdoes it hold up?

The bills alone are 30andthedimesadd30 and the dimes add6, so a total of 36issensible;600centsisexactly36 is sensible; 600 cents is exactly6, confirming $36.

Another way: Convert everything to cents: 3 bills = 3000 cents, 60 dimes = 600 cents, total 3600 cents = $36.

Standardsmin grade 2
  • 2.MD.C.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies — Finding and adding the values of ten-dollar bills and dimes.
💡Takeaway. Ten dimes bundle up into a dollar, so a pile of dimes is just a few dollars to add to your bills!
Variant 11 hard answer: $27

Sophie has 2 ten-dollar bills and 70 dimes. How much money does Sophie have in all?

Show solution
1 · Understandwhat's really being asked

Sophie has 2 ten-dollar bills and 70 dimes. Find the total amount of money.

Givens
  • There are 2 ten-dollar bills.
  • There are 70 dimes (each dime is 10 cents).
  • Ten dimes make one dollar.
Unknowns
  • The total amount of money in all.
Constraints
  • Money is counted in dollars and cents; 100 cents make a dollar.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

There are two kinds of money, so I find the value of each group separately by tracking its units (bills to dollars, dimes to dollars) and then add the two totals.

3 · Execute3 carry out the plan

1Value of the ten-dollar bills

#7 Identify Subproblems 2.MD.C.8
Each ten-dollar bill is worth 10,andthereare2ofthem,sothebillsareworth2times10, and there are 2 of them, so the bills are worth 2 times10, which is $20.
2×$10=$202 \times \$10 = \$20
Counting by tens gives the dollar value of the bills.

2Value of the dimes

#8 Analyze the Units 2.MD.C.8
Each dime is 10 cents, and ten dimes make one dollar. So 70 dimes are 700 cents, which is $7.
70×10 cents=700 cents=$770 \times 10\text{ cents} = 700\text{ cents} = \$7
Because ten dimes equal a dollar, the dimes bundle into whole dollars, the same way ten hundreds make a thousand.

3Add the two amounts

#7 Identify Subproblems 2.MD.C.8
Combine the bills and the dimes: 20fromthebillsplus20 from the bills plus7 from the dimes is $27.
$20+$7=$27\$20 + \$7 = \$27
The total money is just the dollar amounts of each group added together.
Answer: $27
4 · Reviewdoes it hold up?

The bills alone are 20andthedimesadd20 and the dimes add7, so a total of 27issensible;700centsisexactly27 is sensible; 700 cents is exactly7, confirming $27.

Another way: Convert everything to cents: 2 bills = 2000 cents, 70 dimes = 700 cents, total 2700 cents = $27.

Standardsmin grade 2
  • 2.MD.C.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies — Finding and adding the values of ten-dollar bills and dimes.
💡Takeaway. Ten dimes bundle up into a dollar, so a pile of dimes is just a few dollars to add to your bills!
Variant 12 hard answer: $49

Sophie has 4 ten-dollar bills and 90 dimes. How much money does Sophie have in all?

Show solution
1 · Understandwhat's really being asked

Sophie has 4 ten-dollar bills and 90 dimes. Find the total amount of money.

Givens
  • There are 4 ten-dollar bills.
  • There are 90 dimes (each dime is 10 cents).
  • Ten dimes make one dollar.
Unknowns
  • The total amount of money in all.
Constraints
  • Money is counted in dollars and cents; 100 cents make a dollar.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

There are two kinds of money, so I find the value of each group separately by tracking its units (bills to dollars, dimes to dollars) and then add the two totals.

3 · Execute3 carry out the plan

1Value of the ten-dollar bills

#7 Identify Subproblems 2.MD.C.8
Each ten-dollar bill is worth 10,andthereare4ofthem,sothebillsareworth4times10, and there are 4 of them, so the bills are worth 4 times10, which is $40.
4×$10=$404 \times \$10 = \$40
Counting by tens gives the dollar value of the bills.

2Value of the dimes

#8 Analyze the Units 2.MD.C.8
Each dime is 10 cents, and ten dimes make one dollar. So 90 dimes are 900 cents, which is $9.
90×10 cents=900 cents=$990 \times 10\text{ cents} = 900\text{ cents} = \$9
Because ten dimes equal a dollar, the dimes bundle into whole dollars, the same way ten hundreds make a thousand.

3Add the two amounts

#7 Identify Subproblems 2.MD.C.8
Combine the bills and the dimes: 40fromthebillsplus40 from the bills plus9 from the dimes is $49.
$40+$9=$49\$40 + \$9 = \$49
The total money is just the dollar amounts of each group added together.
Answer: $49
4 · Reviewdoes it hold up?

The bills alone are 40andthedimesadd40 and the dimes add9, so a total of 49issensible;900centsisexactly49 is sensible; 900 cents is exactly9, confirming $49.

Another way: Convert everything to cents: 4 bills = 4000 cents, 90 dimes = 900 cents, total 4900 cents = $49.

Standardsmin grade 2
  • 2.MD.C.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies — Finding and adding the values of ten-dollar bills and dimes.
💡Takeaway. Ten dimes bundle up into a dollar, so a pile of dimes is just a few dollars to add to your bills!