One number is 8 more than 1/2 of another number. The sum of the numbers is 23. What are the numbers?

10 and 13

Step-by-step explanation:

Let the two numbers be p and q. p = (1/2) q + 8. p + q = 23. Substituting (1/2) q + 8 for p, we get (1/2) q + 8 + q = 23.

First, subtract 8 from both sides, obtaining (1/2) q + q = 15.

Next, mult. all terms by 2 to eliminate the fraction (1/2) : q + 2q = 30.

Then 3q = 30, and q = 10. Then p = (1/2) (10) + 8 = 5 + 8 = 13.

The numbers are 10 and 13.