SOLUTION: "The product of two consecutive integer is 80 more than 15 times the larger integer." What do I do to solve this problem?

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

RELATED QUESTIONS
the product of two consecutive integers is 80 more than 15 times the larger integer. what (answered by mananth)

the product of two consecutive odd integers is fourteen more than three times the larger... (answered by TimothyLamb)

The product of two consecutive positive integers is 32 more than three times the larger... (answered by CubeyThePenguin)

The product of two consecutive positive integers is 39 more than nine times the larger... (answered by josgarithmetic)

The product of two consecutive positive integers is 21 more than three times the larger... (answered by josgarithmetic)

Find two consecutive even integers whose product is 24 more than 8 times the larger... (answered by stanbon)

the product of two consecutive positive integers is 80 more than 15 times larger the... (answered by TimothyLamb)

The product of two consecutive positive integers is 27 more than five times the larger... (answered by TimothyLamb)

the product of two consecutive positive integers is 52 more than 8 times the larger... (answered by hkwu)