# The sum of the digits of a two-digit number is 12.the value of the number is 6 times the units digit.What is the number?

1
by kAYEHyun

2015-02-09T21:46:20+08:00

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Let x be the units digit and y be the tens digit of the number.

y + x = 12
10y + x = 6x

10y = 6x -x
10y = 5x
10y - 5x = 0 (this is transposing, if a term goes to the other side, it's sign will change.)

( multiply 10 to all the terms in the first equation so that if y multiplied by 10 is subtracted by 10y in the second equation, the result will be 0. )
10y +10x = 120
-
10y - 5x = 0
15x = 120
(divide both by 12)

x = 8
Substitute x to any of the two equations, say the first equation.

10y + 10x = 120
10y + 10 (8) = 120
10y + 80 = 120
10y + 80 - 80 = 120 - 80
10y + 0 = 40
10y = 40
y = 4

Therefore, the number is 48.