The sum of two integers is 23 and the positive difference of the same two integers is 13. What is the product of these two integers?

A) 90 B) 75

C) 46 D) 299

A) 90

Step-by-step explanation:

"The sum of two integers is 23" becomes

a + b = 23

"the positive difference of the same two integers is 13" becomes

a - b = 13 (difference means subtract)

Now solve the system ...

a + b = 23

a - b = 13 * use addition or elimination method, since b has opposite coefficients ...

2a = 36 (we add the two equations together)

a = 18 (divide by 2 on both sides)

Since a = 18, 18 + b = 23, gives us b = 5. (18 + 5 = 23)

ab = (18) (5) = 90