SOLUTION: A 2 digit no is such that the product of its digits is 35. If 18 is added to the Number, the digits interchange their places. Find the Number.

Question 601346: A 2 digit no is such that the product of its digits is 35. If 18 is added to the Number, the digits interchange their places. Find the Number.
Answer by flame8855(424) (Show Source): You can put this solution on YOUR website!
let x be the ones digit and y be the tenth digit
xy=35
the number is equal to 10y+x
if 18 is added
10y +x+ 18
digit are interchanged so the number is xy, 10x+y
so 10y +x+ 18 = 10x+y
solve the two equations
9y-9x+18=0
y-x-2=0
x=y-2
xy=35
(y-2)(y)=35
y^2 -2y-35 =0
(y-7) (y+5) =0
y=7 so x = 5
y = -5 is rejected since -5 is negative
the number is 35

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