Question 277161
find a number whose half exceeds its third by the sum of its digits. give the formula.

x = a number
y = sum of x's digits

half exceeds its third by an amount (in this case the amount is the sum of the digits of the number) means that the half equals the third plus the amount

1/2 * x = 1/3 * x + y (convert to 6ths)
3/6 * x = 2/6 * x + y
1/6 * x = y (multiply both sides by 6)
x = 6y
so that means the number will be 6 times the sum of its digits

example answer would be 54, 6 * (5 + 4) = 6 * 9 = 54
                       27 = 18 + 9 = 27