Question

The difference between two numbers is 28. The larger number is 8 less than twice the smaller number. Find both numbers. [Only an algebraic solution can receive full credit.]​

Answer 1

The larger number is 64 and the smaller number is 36.

Explanation:

Set up an equation to find the value of one number, x, and use that find find the value of the second number. Use x as the variable for the smaller number. The larger number is 2 times the smaller number minus 8, so the part of the equation for the larger number would be 2x-8. Then because the difference between the two numbers is 28, you would subtract the smaller number, x, from the larger number equation.

The equation should look like this: 2x-8-x=28

Combine like terms to get this: x-8=28

Add 8 to both sides of the equation: x=36

Because x represents the smaller number, the smaller number is 36. To find the larger number, just plug the numbers into the large number equation from earlier: 2(36)-8 The answer for the large number is 64, and the difference between 64 and 36 is 28, proving the answer correct.