Best friends Olivia and Sylvia both get a weekly allowance. Olivia’s and Sylvia’s allowances are in the ratio 2:3

Question

. If Sylvia gets $21 one week, how much did Olivia get? Use a tape diagram to help organize your thinking.(1 point)
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Answer 1

To solve for Olivia's allowance given the ratio of their allowances and Sylvia's allowance, we can break down the problem.

1. Understanding the Ratio: The ratio of Olivia's allowance to Sylvia's allowance is 2:3. This means for every 2 parts of Olivia's allowance, Sylvia gets 3 parts.

2. Finding the Total Parts: The total parts in the ratio are $2+3=5$ parts.

3. Determining the Value of One Part: If Sylvia receives $21 (which represents 3 parts), we can find the value of one part by dividing Sylvia's allowance by the number of parts she has: $$\text{Value of one part}=\frac{21}{3}=7$$

4. Calculating Olivia's Allowance: Now that we know the value of one part, we can find Olivia's allowance. Since Olivia gets 2 parts, we multiply the value of one part by 2: $$\text{Olivia's allowance}=2\times 7=14$$

Therefore, Olivia received $14.