Question

The difference between two numbers is 20. Three times the smaller number is 44 more than the larger number. What are the numbers?

Answer 1

To find the two numbers, we can set up two equations from the given information. After solving the system of equations, we find that the smaller number is 32 and the larger number is 52.

Step-by-step explanation:

The question asks us to find two numbers where their difference is 20, and three times the smaller number is 44 more than the larger number. To solve this, we can set up two equations based on the information given:

• Let the smaller number be x, and the larger number be y.
• The difference between them is 20: y - x = 20.
• Three times the smaller number is 44 more than the larger number: 3x = y + 44.

Now we can solve the system of linear equations:

1. From the first equation, we get y = x + 20.
2. Substitute y in the second equation: 3x = (x + 20) + 44.
3. Simplify: 3x = x + 64.
4. Solve for x: x = 32.
5. Find y: y = 32 + 20 = 52.

Therefore, the two numbers are 32 (the smaller number) and 52 (the larger number).