Question

the sum of two numbers is 58 and the difference is 6. what are the numbers?
larger number:
smaller number:

Explanation:

Step1: Define variables

Let the larger number be \( x \) and the smaller number be \( y \).

Step2: Set up equations

We know that the sum of the two numbers is 58, so \( x + y = 58 \). Also, the difference is 6, so \( x - y = 6 \).

Step3: Solve the system of equations

Add the two equations together: \( (x + y) + (x - y) = 58 + 6 \).
Simplify the left side: \( 2x = 64 \).
Divide both sides by 2: \( x = \frac{64}{2} = 32 \).

Step4: Find the smaller number

Substitute \( x = 32 \) into the first equation \( x + y = 58 \): \( 32 + y = 58 \).
Subtract 32 from both sides: \( y = 58 - 32 = 26 \).

Answer:

Larger number: 32
Smaller number: 26