Question

The difference of two numbers is 18. The first number is 2 more than three times the second. What are the two numbers?

Answer 1

x=26, y=8

Explanation:

x-y =18

x=3y +2

3y +2 - y =18

2y =18 - 2

2y =16

y=16 :2

y=8 (the second number

x=3 ×8 +2 =26 (the first number

Answer 2

The two numbers are 4 and 22.

Explanation:

Let the two numbers be x and y. Let y be the smaller number.

x - y = 18

2y + 3x = 74

Solve the first equation for either variable and plug it into the second equation.

Solving for y: x = y + 18

2y + 3(y + 18) = 74

Simplify.

2y + 3y + 54 = 74

5y + 54 = 74

5y = 20

y = 4

Go back and solve for x.

x - y = 18

x - 4 = 18

x = 22

The two numbers are 4 and 22.

Check using both equations.

The difference between 22 and 4 is 18.

Twice the smaller is 8. Three times the larger is 66. The sum of 8 and 66 is 74.