b) The sum of two numbers is 39 . If the greater number is 5 more than the orget one, find the numbers. The sum of two numbers is 54 . If the smaller number is 6 less than thee geser one, find the numbers.

Let's break down the two parts of the problem step by step. ### Part 1: The sum of two numbers is 39 1. **Define the variables:** - Let \( x \) be the greater number. - Let \( y \) be the smaller number. 2. **Set up the equations based on the problem statement:** - From the first condition, we have: \[ x + y = 39 \quad (1) \] - From the second condition, we know that the greater number is 5 more than the smaller number: \[ x = y + 5 \quad (2) \] 3. **Substitute equation (2) into equation (1):** \[ (y + 5) + y = 39 \] Simplifying this gives: \[ 2y + 5 = 39 \] \[ 2y = 39 - 5 \] \[ 2y = 34 \] \[ y = 17 \] 4. **Find \( x \) using equation (2):** \[ x = y + 5 = 17 + 5 = 22 \] So, the two numbers are \( 22 \) (greater) and \( 17 \) (smaller). ### Part 2: The sum of two numbers is 54 1. **Define the variables:** - Let \( a \) be the greater number. - Let \( b \) be the smaller number. 2. **Set up the equations based on the problem statement:** - From the first condition, we have: \[ a + b = 54 \quad (3) \] - From the second condition, we know that the smaller number is 6 less than the greater number: \[ b = a - 6 \quad (4) \] 3. **Substitute equation (4) into equation (3):** \[ a + (a - 6) = 54 \] Simplifying this gives: \[ 2a - 6 = 54 \] \[ 2a = 54 + 6 \] \[ 2a = 60 \] \[ a = 30 \] 4. **Find \( b \) using equation (4):** \[ b = a - 6 = 30 - 6 = 24 \] So, the two numbers are \( 30 \) (greater) and \( 24 \) (smaller). ### Summary of Results: - For the first part, the numbers are \( 22 \) and \( 17 \). - For the second part, the numbers are \( 30 \) and \( 24 \).