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
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