The product of two consecutive even integers is 34 less than 7 times their sum, how do you find the two integers?

1 Answer
Jul 5, 2015

Answer:

Let's call the numbers #2nand2n+2# with #n# an integer, and the #2# to make sure it's even.

Explanation:

Then we translate the rest of the conditions:
Product: #P=2n*(2n+2)=4n^2+4n#
Sum: #S=2n+(2n+2)=4n+2#

Now #P=7*S-34#

Substituting:
#4n^2+4n=7*(4n+2)-34->#
#4n^2+4n=28n+14-34->#

Everything to one side:
#4n^2-24n+20=0->#

Divide everything by #4# to make life easier:
#n^2-6n+5=0-># factorise:
#(n-1)(n-5)=0->n=1orn=5#

So the numbers are #2and4# or #10and 12#

Checking:
#2*4=7*(2+4)-34->8=42-34# check!
#10*12=7*(10+12)-34->120=154-34# check!