the difference between two numbers is 18. three times the larger number plus twice the smaller is 74. find the two numbers

Question

i don't understand how to do this

Answer 1

Let x is the larger number and y is the smaller number.

The difference is 18

x - y = 18.

 

Three times the sum of the larger number plus two times the smaller number is 74.

3x + 2y = 74.

 

We write the two equations and solve for the variables x and y.

x - y = 18

3x + 2y = 74.

Elimination method.

We multiply the first equation by 2 and add the two equations.

    2x - 2y = 36

+

     3x +2y =74

     5x        =110

 

 

x = 22.

 

We substitute in the first equation and find

22-y=18

y=4.

 

The larger number is 22 and the smaller number is 4.

 

Questions?