Today, Reza ate 20 grapes, which was 400% as many grapes as he ate yesterday. Explain how to use equivalent ratios to find the number of grapes Reza ate yesterday.

1 answer

To solve the problem using equivalent ratios, we start by understanding what is meant by "400% as many grapes."

  1. 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.
  2. 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).
  3. 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: \[ 20 = 4x \]
  4. 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.