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

Question

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.
Set Up the Ratio:

Let
represent the number of grapes Reza ate yesterday.
The relationship can be expressed as the ratio
(today to yesterday).
Set Up the Equation:

According to the ratio, we can write the equation:
Since we know Reza ate 20 grapes today, we can substitute that into our equation:
Solve for
:

Now, we will solve for
:

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.

Answer 1

To summarize the solution clearly step by step:

1. Understanding "400% as many grapes":

   • 400% means 400 out of 100 or equivalently 4 out of 1.
   • This means that for every 1 grape Reza ate yesterday, he ate 4 grapes today.

2. Setting Up the Ratio:

   • Let \( x \) represent the number of grapes Reza ate yesterday.
   • The relationship can be expressed as the ratio of grapes Reza ate today to the grapes he ate yesterday, which is \( \frac{4}{1} \).

3. Setting Up the Equation:

   • According to the ratio, we have the equation: \[ \frac{\text{grapes today}}{\text{grapes yesterday}} = \frac{4}{1} \]
   • Since we know Reza ate 20 grapes today, we can substitute that into our equation: \[ \frac{20}{x} = \frac{4}{1} \]

4. Solving for \( x \):

   • Cross-multiply to solve for \( x \): \[ 20 \cdot 1 = 4 \cdot x \] \[ 20 = 4x \]
   • Now, divide both sides by 4: \[ x = \frac{20}{4} = 5 \]

5. Conclusion:

   • Therefore, Reza ate 5 grapes yesterday.

This process allows us to translate a percentage increase into a solvable ratio and find the quantity in question.