SOLUTION: The product of two consecutive even integers is 60 more than twice the larger. Find the first integer

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Question 980662: The product of two consecutive even integers is 60 more than twice the larger. Find the first integer
Found 2 solutions by josgarithmetic, Cromlix:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
n is any integer.
Two consecutive even integers are 2n and 2n+2.

2n%282n%2B2%29=60%2B2%282n%2B2%29, the description put into an equation.

n%282n%2B2%29=30%2B%282n%2B2%29
n%28n%2B1%29=15%2B%28n%2B1%29
n%5E2%2Bn=15%2Bn%2B1
n%5E2=16
n=0%2B-+4

The numbers may be -4 and -2;
or 4 and 6.

Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,
Make the two consecutive
integers be n + 1, n + 3
(n + 1)(n + 3) = 2(n + 3) + 60
Multiply out
n^2 + 4n + 3 = 2n + 6 + 60
Collect like terms and put in form
ax^2 + bx + c = 0
n^2 + 2n - 63 = 0
Factorise
(n - 7)(n + 9) = 0
n + 9 = 0
n = -9 (no answer as -ve)
n - 7 = 0
n = 7
Two numbers are. 8 and 10
hope this helps:-)