SOLUTION: a two digit number is obtained by multiplying the sum of the digits by 8.also it is obtained by multiplying the difference of the digits by 14 and adding 2 find the number

Question 1035569: a two digit number is obtained by multiplying the sum of the digits by 8.also it is obtained by multiplying the difference of the digits by 14 and adding 2 find the number
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Call the two-digit number xy, where x is the tens and y is the ones. Its value is 10x + y.
Then we can write
8(x + y) = 10x + y
and
14(x - y) + 2 = 10x + y
Simplifying these we get
8x + 8y = 10x + y
7y = 2x (or 14y = 4x)
and
14x - 14y + 2 = 10x + y
4x + 2 = 15y
Substitute from above and get
14y + 2 = 15y
y = 2
so then x = 7
Your number is 72.
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