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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)

1 answer

To solve the problem, we start by analyzing the ratio of Olivia's and Sylvia's allowances, which is 2:3. This means for every 2 parts Olivia receives, Sylvia receives 3 parts.

Given that Sylvia receives $21, we need to figure out how much each "part" of the allowance is worth first.

  1. Set up the parts based on the ratio:

    • Let Olivia's parts = 2
    • Let Sylvia's parts = 3

  2. Find the value of one part: Since Sylvia's allowance represents 3 parts and she gets $21, we can calculate the value of one part by dividing her amount by 3: \[ \text{Value of one part} = \frac{21}{3} = 7 \]

  3. Now, calculate Olivia's allowance: Olivia receives 2 parts. Therefore: \[ \text{Olivia's allowance} = 2 \times 7 = 14 \]

So, Olivia received $14.

Tape Diagram Representation

To visualize this with a tape diagram:

Olivia:   |---|---| (2 parts)
Sylvia:   |---|---|---|---|---| (3 parts)

Each segment = $7

Olivia:   | $7 | $7 |  (Total = $14)
Sylvia:   | $7 | $7 | $7 | (Total = $21)

In summary, Olivia received $14, and this is consistent with the initial ratio of their allowances.