SOLUTION: The larger of two positive integers is five more than twice the smaller integer. The product of the integers is 52. What are the two integers?

Question 246073: The larger of two positive integers is five more than twice the smaller integer. The product of the integers is 52. What are the two integers?
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
let x=first integer and y= second integer
x=2y+5
xy=52
substitute 2y+5 for x in the second equation
(2y+5)*y=52
2y^2+5y=52
divide by 2
y^2+5/2=26
we will complete the square
take (5/2)/2 and square it
(5/4)^2=25/16
convert 26 to improper fraction with 16 as the denominator
y^2+5/2=416/16
add 25/16 to both sides
y^2+5/2+25/16=416/16+25/16
y^2+5/2+25/16=441/16
factor left hand side
(y+5/4)^2=441/16
|y+5/4|=21/4
y+5/4=-21/4
y+5/4=21/4
subtract 5/4 from both sides
y=-26/4=-13/2
y=16/4=4
only 4 is a positive integer
4*x=52
x=13
so the two integers are 4 and 13
check
2(4)+5=8+5=13
ok

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