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

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

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.
 
Taking the square root of 7920 gives 88.99....
 
88 and 90 are the room numbers.

Comments

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