The difference of the squares of two positive consecutive even integers is 36. find the integers. use the fact that, if x represents an even integer, then x+2 represents the next consecutive even integer.

Hello from MrBillDoesMath!

8 and 10

Discussion:

Let x and x+2 be as described in the Question. Then

(x+2)^2 - x^2 = 36             => (x+2)^2 = x^2 + 2x + 4

x^2 + 4x + 4 - x^2 =36      => the x^2 terms cancel

4x + 4 = 36                        => subtract 4 from both sides

4x = 36 -4 - 32                  => divide both sides by 4

x = 32/4 = 8

So the integers are 8 and 10 (8+2)

Check: 10^2 - 8^2 = 100 -64 - 36.

Thank you,

MrB

x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)