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.
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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: \[ 3x = 21 \]
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Solve for \( x \): To find \( x \): \[ x = \frac{21}{3} = 7 \]
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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 \( x \): \[ \text{Olivia's allowance} = 2 \times 7 = 14 \]
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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.