Question

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)

Answer 1

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.