Question 821297: "The product of two consecutive integer is 80 more than 15 times the larger integer." What do I do to solve this problem? Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! let x and x+1 be the consecutive integers, then
x * (x+1) = 15 * (x+1) + 80
x^2 + x = 15x + 15 + 80
x^2 -14x -95 = 0
this quadratic factors into
(x-19) * (x+5) = 0 and
x = 19 or -5
there fore we have two sets of solutions
solution set 1 is 19 and 20
solution set 2 is -5 and -4
let's check the solutions
19*20 = 15*20 + 80
380 = 300 + 80
380 = 380
solution set 1 checks
-5*-4 = 15 * (-4) + 80
20 = -60 + 80
20 = 20
solution set 2 checks
