Question

The sum of two numbers is eighteen. The total of three times the smaller and twice the larger is forty-four. Find the two numbers.

Answer 1

• The numbers are 8 and 10.

Explanation:

Let the numbers be x and y.

The sum of two numbers is eighteen:

• x + y = 18

The total of three times the smaller and twice the larger is forty-four:

• 3x + 2y = 44

Solve the system by substitution:

• x = 18 - y

Substitute x and solve for y:

• 3(18 - y) + 2y = 44
• 54- 3y + 2y = 44
• 54 - y = 44
• y = 54 - 44
• y = 10

Find x:

• x = 18 - 10
• x = 8