Question

The difference of two is 4. The larger is 8 less than twice the smaller. What are the two numbers ?

Answer 1

{12, 16}

Explanation:

The difference of two numbers (x and y) is 4. Thus, if y is the larger, then y - x = 4. Also, y = 2x - 8.

So we need to solve the system of linear equations

y - x = 4

y = 2x - 8

Subbing 2x - 8 for y, in the first equation, we get (2x - 8) - x = 4, or

x - 8 = 4, and conclude that x = 12. Then, because y - x = 4, y must be 16.

The numbers are 12 and 16.