Question

2 1/4 was subtracted twice from a number; then 1/8 was subtracted three times and 2/3 was subtracted twice. The resulting number is 3 11/24 . Find the number

Answer 1

We will call the unknown number x.
x - 2 1/4 - 1/8(3) - 2/3(2) = 3 11/24
x - 2 1/4 - (1/8)(3/1) - (2/3)(2/1) = 3 11/24
x - 2 1/4 - 3/8 - 4/3 = 3 11/24
We need a common denominator.  24 is the first number that 4, 8 and 3 all both divide evenly into.
x - 2 6/24 - 9/24 - 32/24 = 3 11/24
x - 2 15/24 - 32/24 = 3 11/24
x - 2 47/24 = 3 11/24
x - 3 23/24 = 3 11/24
Cancel the 3 23/34 by adding to both sides:
x - 3 23/24 + 3 23/24 = 3 11/24 + 3 23/24
x = 6 34/24 = 7 10/24 = 7 5/12