Question

two numbers total 41 and have a difference of 7. find the two numbers.
the larger number is \\(\square\\), and the smaller number is \\(\square\\).

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 41, so \( x + y = 41 \). Also, the difference between the two numbers is 7, so \( x - y = 7 \).

Step3: Solve the system of equations

Add the two equations together: \( (x + y) + (x - y) = 41 + 7 \). Simplifying the left side gives \( 2x \), and the right side gives 48. So \( 2x = 48 \), which means \( x = \frac{48}{2} = 24 \).

Step4: Find the smaller number

Substitute \( x = 24 \) into the first equation \( x + y = 41 \). So \( 24 + y = 41 \), and then \( y = 41 - 24 = 17 \).

Answer:

The larger number is \( 24 \), and the smaller number is \( 17 \).