5/12 of a number is subtracted from 3/4 of the number. Their positive difference is 7 less than 5/6 of the number. Find the number

3 answers

Let's call the number we're trying to find "x".

First, let's set up the equation for the information given in the problem:

3/4x - 5/12x = (5/6)x - 7

To solve for x, we need to simplify this equation:

Multiplying everything by 12 to get rid of the fractions:

9x - 5x = 10x - 84

Simplifying:

4x = 84

x = 21

Therefore, the number we're looking for is 21.
well I got x = 14
check
(3/4)(14) - (5/12)(14) = (5/6)(14) - 7 ???
21/2 - 35/6 = 35/3 - 7
63/6 -35/6 = 70/6 - 7
28/6 = 70/6 - 7
-42/6 = -7
sure enough
I think

9x - 5x = 10x - 84

Simplifying:

6x = 84

x = 14

Therefore, the number we're looking for is 14.