Question

The larger of two numbers is 32 more than three times the smaller number. If the sum of the two numbers is 72, what is the value of the larger number?

Answer 1

To find the larger number, we set up a system of equations with two variables representing the two numbers. After solving, we determine that the larger number is 62.

Step-by-step explanation:

The student is asked to solve a problem where two numbers are given such that the larger number is 32 more than three times the smaller number, and their sum is 72. To find the values of the two numbers, we set up a system of equations:

• Let the smaller number be x.
• Then the larger number is 3x + 32.
• The sum of the two numbers is x + (3x + 32) = 72.

Solving this system:

1. Combine like terms: 4x + 32 = 72.
2. Subtract 32 from both sides: 4x = 40.
3. Divide both sides by 4: x = 10.
4. Now that we have the smaller number, we plug it into the expression for the larger number: 3(10) + 32 = 62.

Therefore, the value of the larger number is 62.