Question

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

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.