SOLUTION: If the product of two consecutive integers is decreased by 20 times the greater integer. The result is 442. Find the integers.

Question 370040: If the product of two consecutive integers is decreased by 20 times the greater integer. The result is 442. Find the integers.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Consecutive integers are 1 apart from each other. So if
x = the first integer
then
x+1 = the next integer

The product of two consecutive integers:
x*(x+1)
The product of two consecutive integers is decreased by 20 times the greater integer:
x*(x+1) - 20*(x+1)
The product of two consecutive integers is decreased by 20 times the greater integer [is} 442:
x*(x+1) - 20*(x+1) = 442

Now that we have translated the problem into an equation we can solve it. First we simplify each side:

This is a quadratic equation so we want one side to be zero. So we'll subtract 442 from each side:

Now we factor (or use the Quadratic Formula):
(x-33)(x+14) = 0
From the Zero Product Property we know that this (or any) product can be zero only if one (or more) factors is zero. So:
x-33 = 0 or x+14 = 0
Solving these we get:
x = 33 or x = -14

These are not consecutive integers. But they are not supposed to be! "x" is the first of the two integers. x+1 is the other integer. So we have two sets of answers, one for when x = 33 and the other for when x = -14:
33 and 34
or
-14 and -13

RELATED QUESTIONS
if the product of two consecutive integers is decreased by 20 times the greater integer,... (answered by Paul)

if the product of two consecutive integers is decreased by 20 times the greater integer,... (answered by jojo14344,KnightOwlTutor)

Find two consecutive even integers whose product is 288. A number is increased by 4... (answered by ankor@dixie-net.com)

the product of two consecutive even integers decreased by seven times the greater integer (answered by ankor@dixie-net.com)

if the product of two consecutive odd integers is decreased by one third the lessre the... (answered by stanbon)

If the product of two consecutive odd integers is decreased by one-third the lesser... (answered by checkley71)

if the product of two consecutive odd integers is decreased by 3, the result is 12. find... (answered by checkley77)

if the product of two consecutive odd integers is decreased by 3 the result is... (answered by vleith)

If the product of two consecutive even integers is increased by lesser integer, the... (answered by greenestamps)