What is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 5 less than 5 times the largest integer?

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(1) Answers

abbiepalacios

Lets call our integers:
x, x+1 and x+2
the product of the smaller two integers is 5 less than 5 times the largest integer: this means
x*(x+1) +5= (x+2)*5
taking things out of the brackets:
x*x+x+5= 5x+10
putting everything on one side:
x*x+x -5x +5-10= 0
calculating:
x*x+-4x -5= 0
we can put it into brackets:
(x+1)*(x-5)=0
So we have x=-1 (which can't be, it has to be positive)
or x=5, which is the answer!