SOLUTION: The product of two consecutive positive even integers is 80. Find the integers.

Question 231257: The product of two consecutive positive even integers is 80. Find the integers.
Answer by texttutoring(324) (Show Source): You can put this solution on YOUR website!
We need 2 Equations with 2 Variables.
Consecutive even numbers have a difference of 2. For example, 4-2=2. 6-4=2,8-6=2.
Let x= the larger number
Let y= the smaller number

Eqn 1: x-y=2
Eqn 2: x*y=80
Rearrange Eqn 1 to isolate for x:
Eqn 1: x=2+y
Sub this into Eqn 2:
(2+y)*y=80
2y+y^2=80
y^2+2y-80=0
Factor (think, what numbers multiply to -80 and add up to +2?:
(y+10)(y-8)=0
y=-10 or y=8
Sub the positive answer (+8) into Eqn 1:
x-8=2
x=10
The two numbers are 10 and 8.
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