If x is 80% of y,what percent of x is y?

Options

A. 75%
B. 80%
C. 100%
D. 125%

Answer

To solve the problem step by step, we start with the information given in the question:

### Step 1: Understand the relationship between x and y.
We are given that \( x \) is 80% of \( y \). This can be mathematically expressed as:
\[ x = 0.8y \]

### Step 2: Express y in terms of x.
To find out what percent of \( x \) is \( y \), we need to express \( y \) in terms of \( x \). From the equation \( x = 0.8y \), we can rearrange it to find \( y \):
\[ y = \frac{x}{0.8} \]
This simplifies to:
\[ y = \frac{x}{\frac{8}{10}} = \frac{10x}{8} = \frac{5x}{4} \]

### Step 3: Set up the equation to find the percentage.
We want to find what percent of \( x \) is \( y \). We can express this as:
\[ \text{Percentage} = \left( \frac{y}{x} \right) \times 100 \]

### Step 4: Substitute the value of y.
Now substitute \( y \) from Step 2 into the percentage equation:
\[ \text{Percentage} = \left( \frac{\frac{5x}{4}}{x} \right) \times 100 \]

### Step 5: Simplify the equation.
The \( x \) in the numerator and denominator cancels out:
\[ \text{Percentage} = \left( \frac{5}{4} \right) \times 100 \]

### Step 6: Calculate the percentage.
Now, calculate the value:
\[ \text{Percentage} = \frac{5 \times 100}{4} = \frac{500}{4} = 125 \]

### Conclusion:
Thus, \( y \) is 125% of \( x \).

### Final Answer:
So, the answer to the question "what percent of \( x \) is \( y \)?" is:
\[ \text{125%} \]

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