Question

Using the 3-step method, solve the problem involving two numbers. The larger number is one more than three times the smaller number. The sum of the numbers is 49. Find the two numbers.

Answer 1

To solve for two numbers where one is one more than three times the other and their sum is 49, you set up an equation, simplify it, and solve for the smaller number, resulting in the two numbers being 12 and 37.

Step-by-step explanation:

When solving a problem involving two numbers where one number is directly related to another, establishing their relationship with variables is essential. Here's how to solve the problem:

1. Let the smaller number be x. Then, the larger number is 3x + 1.
2. According to the problem, their sum is 49. This gives us the equation x + (3x + 1) = 49.
3. Simplify the equation to get 4x + 1 = 49. Subtract 1 from both sides to get 4x = 48. Then divide both sides by 4 to find x = 12.

Thus, the smaller number is 12, and the larger number, being one more than three times the smaller number, is 3(12) + 1 which equals 37. The two numbers are 12 and 37.