To solve the problem using the given ratio of Olivia's and Sylvia's allowances, we can set up a tape diagram to represent their allowances.
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Understanding the Ratio: Olivia and Sylvia’s allowances are in the ratio \(2:3\). This means for every 2 parts that Olivia gets, Sylvia gets 3 parts.
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Setting Up the Parts: Let's represent Olivia's allowance as \(2x\) and Sylvia's allowance as \(3x\), where \(x\) is the common multiple for their allowances.
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Sylvia's Allowance: We know that Sylvia gets $21 one week. According to our representation, this can be written as: \[ 3x = 21 \]
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Finding \(x\): To find \(x\), we can divide both sides of the equation by 3: \[ x = \frac{21}{3} = 7 \]
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Calculating Olivia's Allowance: Now that we have \(x\), we can find Olivia's allowance: \[ 2x = 2 \times 7 = 14 \]
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Conclusion: Therefore, Olivia's allowance is $14.
Tape Diagram Representation:
To visualize this with a tape diagram:
Olivia's Allowance: |---|---| (2 parts for Olivia)
Sylvia's Allowance: |---|---|---|---|---| (3 parts for Sylvia)
- Each part in the diagram represents $7 (the value of \(x\)).
- Olivia has 2 parts (2 x 7 = $14).
- Sylvia has 3 parts (3 x 7 = $21).
Thus, Olivia received $14.
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