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.

Answer 1

To solve the problem, we can use the ratio of Olivia's and Sylvia's allowances, which is 2:3.

1. Understanding the Ratio: The ratio tells us that for every 2 parts Olivia gets, Sylvia gets 3 parts.

2. Finding Total Parts: In total, the ratio has \(2 + 3 = 5\) parts.

3. Value of Each Part: Since Sylvia gets $21, which corresponds to the 3 parts of the ratio, we can calculate the value of one part: \[ \text{Value of one part} = \frac{21 \text{ dollars}}{3} = 7 \text{ dollars}. \]

4. Calculating Olivia’s Allowance: Olivia’s allowance corresponds to the 2 parts of the ratio. So, we can calculate her allowance as follows: \[ \text{Olivia's allowance} = 2 \times \text{Value of one part} = 2 \times 7 = 14 \text{ dollars}. \]

5. Conclusion: Therefore, Olivia got $14.

Tape Diagram Representation:

You could visualize the problem using a tape diagram like below:

   Olivia's Allowance      |      Sylvia's Allowance
          [---|---]                    [---|---|---]
             2 parts                         3 parts

If Sylvia's allowance is depicted with 3 equal segments ($7 each):

   Olivia's Allowance               Sylvia's Allowance
       [---|---]                           [---|---|---]
         (2)                               (3)
       \ (7) x 2  = $14                   \ (7) x 3  = $21

In this representation, you can see how the ratios relate to their respective amounts, confirming that Olivia received $14.