Question

When three times one number is added to four times the other number, the result is 44. When five times the first number is added to two times the second, the result is 50. What are the numbers?

Answer 1

To solve the system of equations, we can use the method of elimination. The first number is 8 and the second number is 5.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's call the first number x and the second number y.

The first equation can be written as 3x + 4y = 44.

The second equation can be written as 5x + 2y = 50.

To solve the system, we can use the method of substitution or elimination. I will use the method of elimination.

Multiplying the first equation by 5 and the second equation by 3 gives us:

15x + 20y = 220

15x + 6y = 150

Subtracting the second equation from the first equation eliminates x:

20y - 6y = 220 - 150

14y = 70

Dividing both sides of the equation by 14 gives us:

y = 5

Substituting y = 5 into any of the original equations gives us:

3x + 4(5) = 44

3x + 20 = 44

3x = 24

x = 8

So the first number is 8 and the second number is 5.