# math

If the digits of the number are reversed, the number is increased by 36. The sum of the digits in the number is two and one–half times their difference. What is the number?

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1. let the unit digit be y
let the tens digit by x

the original number is 10x + y
the number reversed is 10y + x

10y + x = 10x + y - 36
9y - 9x = -36
x - y = 4

10x+y - (10y+x) = 36
9x - 9y = 36 ----> x - y = 4
x = 4+y

x+y = 2.5(x-y)
2x + 2y = 5(x-y)
2x + 2y = 5x - 5y
7y = 3x
(7/3)y = x

so (7/3)y = 4+y
7y = 12 + 3y
4y = 12
y = 3

if y = 3 , x = 7
the original number is 73

check:
number reversed is 73
73-37 =36 , that's good

sum of digits = 7+3 = 10
2.5(7-3) = 2.5(4) = 10

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2. Where did the 9y - 9x =36 came though?

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