Problem
Mia and Ella are the same age; Liam and Noah are the same age. So the total is twice Ella's age plus twice Liam's age, and that total is 64.
Twins having equal ages means we only have two different numbers to track, not four.
3.OA.A.3Convert To AlgebraElla is 8 older than Liam, so replace Ella with Liam + 8. The equation becomes 2(Liam + 8) + 2(Liam) = 64, which simplifies to 4 times Liam plus 16 equals 64.
Substituting the relationship turns two unknowns into one, so a single equation remains.
3.OA.D.8Convert To AlgebraReplacing Ella with Liam + 8 turns the total into the single-unknown equation .
The four ages already add to 64, and putting in an amount equal to Ella cannot change that total, so the rewritten total must still equal 64.
Ella's age and 'Liam plus 8' are the same number, so the total written with Ella and the total written with Liam plus 8 are two names for one amount, and two totals equal to that one amount are equal to each other and to 64.
Once Ella is written as Liam plus 8, the left side 2 times (Liam plus 8) plus 2 times Liam tidies up to 4 times Liam plus 16.
Two groups of (Liam and 8) is two groups of Liam put together with two groups of 8.
Two groups of 8 is 8 counted twice, which is 16.
Two groups of Liam and two more groups of Liam is Liam counted four times, which is 4 times Liam.
Subtract 16 from 64 to get 48, then divide by 4. Liam is 12, and since Noah is his twin, Noah is also 12.
Undoing 'add 16' then 'times 4' isolates the one unknown age.
3.OA.A.4Convert To AlgebraNoah is 12, and Noah's age is 3 times his younger brother's age. So the younger brother's age is 12 divided by 3, which is 4.
'3 times as old' means the younger child is one-third of Noah's age, found by dividing.
3.OA.A.3Identify SubproblemsWhen twins share an age, four people become just two numbers, so the whole puzzle fits into one neat equation you can solve!