This friends Olivia and Sara both get a weekly allowance. Olivia and Sara allowances are in the radio 2:3 if Sarah gets 21 how much did Aaliyah get use a tape diagram to help organize your thinking?

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
10 days ago

To solve the problem, let's first understand the ratio of Olivia's to Sara's allowances, which is 2:3. This means for every 2 parts that Olivia receives, Sara receives 3 parts.

1. **Identify Sara's allowance**:
According to the problem, Sara's allowance is 21. We can set up the ratio using Sara's allowance. Since Sara's part of the ratio is 3 parts, we can represent her allowance as:
\[
\text{Sara's allowance} = 3x
\]
where \( x \) is the value of one part in the ratio.

Since we know that Sara gets 21, we can write:
\[
3x = 21
\]

2. **Solve for \( x \)**:
To find \( x \):
\[
x = \frac{21}{3} = 7
\]

3. **Find Olivia's allowance**:
According to the ratio, Olivia receives 2 parts. Therefore, her allowance can be represented as:
\[
\text{Olivia's allowance} = 2x
\]
Substitute \( x \):
\[
\text{Olivia's allowance} = 2 \times 7 = 14
\]

4. **Conclusion**:
- Sara's allowance is 21.
- Olivia's allowance is 14.

Therefore, Aaliyah does not appear in this context, and the amount that Olivia gets is 14.

### Tape Diagram Visualization:

You could visualize it with a tape diagram as follows:

- Draw a rectangle divided into 5 equal parts (since 2 (Olivia) + 3 (Sara) = 5)
- Label the first 2 parts as "Olivia" which would equal \( 2 \times 7 = 14 \)
- Label the last 3 parts as "Sara" which would equal \( 3 \times 7 = 21 \)

This diagram demonstrates how the two allowances correspond to a total of 5 parts, illustrating the ratio of allowances clearly.