Question

A two digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number the digits are reversed. Find the numbers

Answer 1

Let x = ones digit
and y = tens digit
then from "a two digit number is 4 more than six times the sum of its digits":
x + 10y = 6(x+y)+4
x + 10y = 6x+6y+4
10y = 5x+6y+4
4y = 5x+4
.
and, from "if 18 is subtracted from the number,the digits are reversed.find the number"
x+10y -18 = y+10x
10y -18 = y+9x
9y -18 = 9x
y -2 = x
.

substitute the above into:
4y = 5x+4
4y = 5(y-2)+4
4y = 5y-10+4
4y = 5y-6
4y+6 = 5y
6 = y
.
substitute above into:
4y = 5x+4
4(6) = 5x+4
24 = 5x+4
20 = 5x
4 = x
.
The number is 64