Expert: Lynn Houston - 1/11/2010

Question
the sum of a digit of a two digit number is one fourth the number. If their difference is 3 . find the number

Answer
x = the ones digit and
y = the 10's digit

So, the number = 10y + x

1/4(10y+x) = x + y
x-y = 3 (or x = 3+y) use this eq to fill in the value of x in the 1st eq.

1/4(10y + 3+y) = 3+y+y
1/4(11y + 3) = 3+2y  multiple everything by 4
11y +3 = 12 + 8y  subtract 8y from both sides
3y + 3 = 12    subtract 3 from both sides
3y = 9   divide by 3
y = 3, therefore x = 6 so the number is 36

the sum of the digits, 9, is 1/4 of 36 and the difference of the digits is 3