To solve the problem using equivalent ratios, we start by understanding what is meant by "400% as many grapes."
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Translate Percentage to a Ratio:
- When we say Reza ate 400% as many grapes today compared to yesterday, we can express this as a ratio.
- 400% means 400 out of 100, which can be simplified to 4 out of 1. This tells us that for every 1 grape Reza ate yesterday, he ate 4 grapes today.
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Set Up the Ratio:
- Let \( x \) represent the number of grapes Reza ate yesterday.
- The relationship can be expressed as the ratio \( 4:1 \) (today to yesterday).
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Set Up the Equation:
- According to the ratio, we can write the equation: \[ \text{Today’s grapes} = 4 \times \text{Yesterday’s grapes} \]
- Since we know Reza ate 20 grapes today, we can substitute that into our equation: \[ 20 = 4x \]
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Solve for \( x \):
- Now, we will solve for \( x \): \[ x = \frac{20}{4} = 5 \]
- Therefore, Reza ate 5 grapes yesterday.
In summary, by understanding the percentage as a ratio and setting up an equation based on that ratio, we found that Reza ate 5 grapes yesterday.