SOLUTION: If the product of two consecutive even integers is increased by lesser integer, the result is 180. Find the integers.

Question 1147129: If the product of two consecutive even integers is increased by lesser integer, the result is 180. Find the integers.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let the two even integers be x and x+2. Then their product, increased by the smaller integer, is

x(x+2)+x = x^2+2x+x = x^2+3x

You want that expression to equal 180:

Solve by factoring. (I leave that to you....)

If a formal algebraic solution is not required, the answer can be found more quickly using trial and error.

Look for two integers whose difference is 3 and whose product is 180, with the restriction that the smaller number is even. The two numbers are 12 and 15.

So the smaller of the two even integers is 12 and the other is 14.

Note that, algebraically, the equation has two solutions, the other of which is -15. However, since the problem is about consecutive even integers, that solution has to be rejected.
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