The room numbers on one side of a school corridor are consecutive positive even integers.

Question

The product of the room numbers for two adjoining rooms on that side is 7920. Find the room numbers.

3/10/2014 | Celsey from Upper Marlboro, MD | 2 Answers | 0 Votes

Answer 1

Hi Celsey;

x(x+2)=7920

Distribute the x...

x²+2x=7920

x²+2x-7920=0

For the FOIL...

FIRST must be (x)(x)=x²

OUTER and INNER must add-up to 2x.

LAST must be (90)(88) or (88)(90)...

(x+90)(x-88)=0

Either or both parenthetical equation(s) must equal zero...

x+90=0....................x-88=0

x=-90.......................x=88

room number cannot be negative. Second answer is only answer.

Room numbers are 88 and (x+2), 90.

Answer 2

Taking the square root of 7920 gives 88.99....

88 and 90 are the room numbers.

3/10/2014 | Ben T.

A somewhat intuitive solution; but can you explain mathematically why it works?

3/11/2014 | Steve S.