If the ratio of y to x is equal to 3 and the sum of y and x is 80, what is the value of y?

Options

A. `-10`
B. `-2`
C. `5`
D. `60`

Answer

To solve the problem step by step, we will follow the information provided in the question.

### Step 1: Understand the ratio
We are given that the ratio of \( y \) to \( x \) is 3. This can be expressed mathematically as:
\[ \frac{y}{x} = 3 \]
From this, we can express \( y \) in terms of \( x \):
\[ y = 3x \]

### Step 2: Use the sum of \( y \) and \( x \)
We are also given that the sum of \( y \) and \( x \) is 80:
\[ x + y = 80 \]

### Step 3: Substitute \( y \) in the sum equation
Now, we can substitute the expression for \( y \) from Step 1 into the sum equation:
\[ x + 3x = 80 \]
This simplifies to:
\[ 4x = 80 \]

### Step 4: Solve for \( x \)
Now, we can solve for \( x \) by dividing both sides by 4:
\[ x = \frac{80}{4} = 20 \]

### Step 5: Find the value of \( y \)
Now that we have \( x \), we can find \( y \) using the expression from Step 1:
\[ y = 3x = 3 \times 20 = 60 \]

### Conclusion
The value of \( y \) is \( 60 \).

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