The number of households in each apartment complex in Gahui's town was surveyed and shown in a pictograph. Find the number of households in the Mugunghwa apartment complex.
Households by Apartment Complex (pictograph)
Complex
Number of households
Dalbit
Chowon
(5 large pictures, 3 small pictures)
Mugunghwa
Taeyang
In the pictograph, each large house picture stands for 100 households and each small house picture stands for 10 households.
Conditions
The Dalbit complex has 40 fewer households than the Chowon complex.
The Taeyang complex has 75 as many households as the Dalbit complex.
The Mugunghwa complex has 120 more households than the Taeyang complex.
Measurement & dataFractions
Show worked solution try it yourself first ✦
1 · Understandwhat's really being asked
A pictograph gives Chowon as 5 large house symbols (100 each) and 3 small (10 each). Three clues link Dalbit, Taeyang, and Mugunghwa to one another. We find Mugunghwa's number of households.
Givens
Chowon (from figure) = 5 large + 3 small house symbols; 1 large = 100, 1 small = 10 households.
Dalbit = Chowon - 40.
Taeyang = 5/7 of Dalbit.
Mugunghwa = Taeyang + 120.
Unknowns
The number of households in the Mugunghwa complex.
Constraints
Household counts are whole numbers.
For Taeyang to be a whole number, Dalbit must be a multiple of 7.
2 · Planchoose the strategy
#11 Work Backwards · also uses: #7 Identify Subproblems
Each clue depends on the previous one, so we solve in order (Chowon -> Dalbit -> Taeyang -> Mugunghwa), each a small subproblem, chaining toward Mugunghwa.
3 · Execute4 carry out the plan
1Read Chowon from the pictograph
#7 Identify Subproblems3.MD.B.3
Chowon shows 5 large house symbols and 3 small ones. Each large is 100 households and each small is 10: 5 x 100 + 3 x 10 = 530.
5×100+3×10=530
Turning the scaled house symbols into a count is the core skill of a scaled pictograph.
2Find Dalbit
#11 Work Backwards3.NF.A.1
Dalbit has 40 fewer households than Chowon, so Dalbit = 530 - 40 = 490. This comes out to 490 = 7 x 70 (a multiple of 7), so taking 5/7 of it in the next step lands on a whole number.
530−40=490
The fraction 5/7 only gives whole households when the whole is split into 7 equal parts, so Dalbit is chosen as a multiple of 7.
3Find Taeyang (5/7 of Dalbit)
#7 Identify Subproblems3.NF.A.1
Taeyang is 5/7 of Dalbit. Splitting Dalbit (490) into 7 equal parts gives 490 / 7 = 70 in each part, and taking 5 of them gives Taeyang = 5 x 70 = 350 households.
Taeyang=75×490=5×70=350
Understanding 5/7 as 5 of the 7 equal parts of a whole is the Grade 3 meaning of a fraction.
🧠 Why? · Feynman
Five sevenths of Dalbit's 490 households is Taeyang's 350 households.
Why?
Splitting Dalbit's 490 into 7 equal parts puts 70 households in each part.
Why?
Since 7 equal parts multiply back up to 490, finding one part means undoing that multiplication by dividing 490 by 7, which gives 70.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
Why?
The 7 parts are cut with nothing left over and nothing overlapping, so they add back up to the whole 490.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
Taking 5 of those equal 70-parts gives 5 times 70, which is 350.
Why?
Five equal groups of 70 is 70 added over and over, and that repeated adding is exactly what 5 times 70 counts.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
4Find Mugunghwa
#11 Work Backwards3.NBT.A.2
Mugunghwa has 120 more households than Taeyang: 350 + 120 = 470.
Mugunghwa=350+120=470
Adding 120 to 350 is a clean within-1000 addition.
Answer:470 households
4 · Reviewdoes it hold up?
Mugunghwa (470) sits sensibly below Chowon (530) and above Taeyang (350). The 5/7 clue forces Dalbit to be a multiple of 7; the value 490 (= 7 x 70) is the multiple of 7 just below Chowon, so Taeyang = 5 x 70 = 350 and Mugunghwa = 350 + 120 = 470, all whole numbers of households.
Another way:Work the fraction as a subproblem first: one seventh of 490 is 70, so 5/7 is 5 x 70 = 350, then add 120 to reach 470 - same answer using Identify Subproblems.
Standardsmin grade 3
3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading Chowon's value from the large and small house symbols.
3.NF.A.1 Understand a fraction as quantity formed by parts of a whole — Interpreting 5/7 of Dalbit as 5 of its 7 equal parts.
3.NBT.A.2 Fluently add and subtract within 1000 — Subtracting 40 and adding 120 along the chain of clues.
💡Takeaway.Solve the clues one after another - read the graph, then 5 of the 7 equal parts, then add 120!