Best friends Olivia and Sylvia both get a weekly allowance. Olivia’s and Sylvia’s allowances are in the ratio 2:3 . If Sylvia gets $21 one week, how much did Olivia get? Use a tape diagram to help organize your thinking.(1 point)

Question

$

Answer 1

To solve the problem using a ratio and a tape diagram, we start with the given ratio of Olivia's allowance to Sylvia's allowance, which is 2:3. This means that for every 2 parts of allowance Olivia gets, Sylvia gets 3 parts.

Let's represent the allowances in parts based on the ratio:

• Olivia's part = 2
• Sylvia's part = 3

Sylvia received $21, which corresponds to the 3 parts in the ratio. To find the value of each part, we divide Sylvia's allowance by the number of parts that correspond to her allowance:

\[ \text{Value of one part} = \frac{\text{Sylvia's allowance}}{\text{Number of parts for Sylvia}} = \frac{21}{3} = 7 \]

Now we can find Olivia's allowance. Since Olivia gets 2 parts:

\[ \text{Olivia's allowance} = \text{Value of one part} \times \text{Number of parts for Olivia} = 7 \times 2 = 14 \]

Therefore, Olivia's allowance is \(\boxed{14}\) dollars.