Three times a larger number added to 4 times a smaller number totals 24. When twice the smaller number is subtracted from twice the larger number

Question

Three times a larger number added to 4 times a smaller number totals 24. When twice the smaller number is subtracted from twice the larger number, the result is 2. What are the two numbers?

Answer 1

Let x = larger number and y = smaller number. The words can be translated to the following two equations.

 

3x + 4y = 24

2x - 2y = 2

 

Leave the top equation alone and multiple the bottom equation by 2.

 

3x + 4y = 24

4x - 4y = 4

 

Add the two equations, thus eliminating y.

 

7x = 28

 

x = 4.

 

Solve one of the equations for y.

y = x - 1

So, y = 4 - 1 = 3

 

The larger number is 4 and the smaller number is 3.