The sum of two number is 161. If one of the numbers is 30% more than the other , then the numbers are

Options

A. 71 and 90
B. 70 and 91
C. 54 and 107
D. 60 and 101

Answer

To solve the problem step by step, we will define the two numbers and set up equations based on the information given.

### Step 1: Define the Variables
Let the two numbers be \( x \) and \( y \).

### Step 2: Set Up the Equations
We know from the problem that:
1. The sum of the two numbers is 161:
\[ x + y = 161 \]
2. One number is 30% more than the other. If we assume \( y \) is the larger number, then:
\[ y = x + 0.3x = 1.3x \]

### Step 3: Substitute the Value of \( y \)
Now, we can substitute the expression for \( y \) from the second equation into the first equation:
\[ x + 1.3x = 161 \]

### Step 4: Combine Like Terms
Combine the terms on the left side:
\[ 2.3x = 161 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides by 2.3:
\[ x = \frac{161}{2.3} \]
Calculating this gives:
\[ x = 70 \]

### Step 6: Find \( y \)
Now that we have \( x \), we can find \( y \) using the equation \( y = 1.3x \):
\[ y = 1.3 \times 70 = 91 \]

### Conclusion
The two numbers are:
\[ x = 70 \quad \text{and} \quad y = 91 \]

### Final Answer
The numbers are 70 and 91.

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