Question

The sum of two numbers is 152. If four times the smaller number is subtracted from the larger​ number, the result is 12. Find the two numbers.

Answer 1

The smaller number is 28 and the larger number is 124.

Explanation:

Let x = the smaller number

Let y = the larger number

x + y = 152

y - 4x = 12 Solve the second equation for y

y = 4x + 12 Substitute 4x + 12 for y into the first equation

x + y = 152

x + 4x + 12 = 152 Combine the x's

5x + 12 = 152 Subtract 12 from both sides of the equation

5x = 140 Divide both side of the equation by 5

x = 28 Substitute 28 for x in the first equation to solve for y

x + y = 152

28 + y = 152 Subtract 28 from both sides of the equation.

y = 124