Sum of two numbers is 150% of the larger number. If smaller number is 16, then what is the value of the larger number?

Options

A. 32
B. 48
C. 24
D. 30

Answer

To solve the problem step by step, let's denote the two numbers as follows:

Let:
- \( x \) = smaller number
- \( y \) = larger number

According to the problem:
1. The sum of the two numbers is 150% of the larger number.
2. The smaller number is given as 16.

### Step 1: Set up the equation
From the information given, we can express the sum of the two numbers:
\[ x + y = 1.5y \]

### Step 2: Substitute the value of the smaller number
Since we know that \( x = 16 \), we can substitute this value into the equation:
\[ 16 + y = 1.5y \]

### Step 3: Rearrange the equation
Now, let's rearrange the equation to isolate \( y \):
\[ 16 = 1.5y - y \]
\[ 16 = 0.5y \]

### Step 4: Solve for \( y \)
To find \( y \), we can multiply both sides of the equation by 2:
\[ 32 = y \]

### Conclusion
The value of the larger number \( y \) is 32.