If U + V = 80 and U : V = 5 : 3, then what is the value of U-V ?

Options

A. 15
B. 25
C. 30
D. 20

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the given information
We are given:
1. \( U + V = 80 \)
2. The ratio \( U : V = 5 : 3 \)

### Step 2: Express U and V in terms of a variable
Since \( U : V = 5 : 3 \), we can express \( U \) and \( V \) as:
- \( U = 5x \)
- \( V = 3x \)

where \( x \) is a common multiplier.

### Step 3: Substitute U and V in the first equation
Now we substitute \( U \) and \( V \) into the equation \( U + V = 80 \):
\[ 5x + 3x = 80 \]

### Step 4: Combine like terms
Combine the terms on the left side:
\[ 8x = 80 \]

### Step 5: Solve for x
Now, divide both sides by 8 to find \( x \):
\[ x = \frac{80}{8} = 10 \]

### Step 6: Find U and V
Now that we have \( x \), we can find \( U \) and \( V \):
- \( U = 5x = 5 \times 10 = 50 \)
- \( V = 3x = 3 \times 10 = 30 \)

### Step 7: Calculate U - V
Now, we need to find \( U - V \):
\[ U - V = 50 - 30 = 20 \]

### Final Answer
Thus, the value of \( U - V \) is \( 20 \).

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