What are two consecutive even integers such that their sum is equal difference of three times the larger and two times the smaller?

1 Answer
Timber Lin · EZ as pi
Dec 31, 2017

#4 and 6#

Explanation:

Let #x= # the smaller of the consecutive even integers. That means the larger of the two consecutive even integers is# x+2# (because even numbers are 2 values apart).

The sum of these two numbers is #x+x+2.#

The difference of three times the larger number and two times the smaller is #3(x+2)-2(x)#.

Setting the two expressions equal to each other:
#x+x+2=3(x+2)-2(x)#

Simplify and solve:
#2x+2=3x+6-2x#
#2x+2=x+6#
#x=4#

So the smaller integer is #4# and the larger is #6.#

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