Question

Best friends Olivia and Sylvia both get weekly allowances. Olivia's and Sylvia's allowances are in the ratio 2 : 3. If Sylvia gets $21 one weeks, how much did Olivia get? Use tape diagram to help organize you thinking.

Answer 1

To set up a tape diagram for this problem, we can represent Olivia's and Sylvia's allowances as two separate bars.

Let's use a pink bar to represent Olivia's allowance and a green bar to represent Sylvia's allowance.

Since the ratio of their allowances is 2:3, we can divide the pink bar into 2 equal parts and the green bar into 3 equal parts.

Now, we know that Sylvia got $21. We can divide the green bar into three equal parts and mark off $21 on one of those parts.

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Olivia Sylvia

Since the green bar represents Sylvia's allowance, we can see that $21 is one part out of three. Therefore, one part represents $21.

Now, we can determine how much each part is worth. We divide Sylvia's allowance by 3 to get the value of each part:

$21 ÷ 3 = $7

We found that each part represents $7.

Now, since the pink bar represents Olivia's allowance and there are 2 parts in the pink bar, we multiply the value of each part by 2 to get Olivia's allowance.

$7 × 2 = $14

Therefore, Olivia received $14 as her allowance.