How many paper clips are there in a box?

Question

In a box of paper clips, 3/8 of them are white, 5/12 of them are red, and the rest are blue. There are 24 more red paper clips than white paper clips.

Answer 1

Let W, R and B represent the numbers of white, red and blue paper clips. In particular R=W+24. N is the total number of paper clips. Substituting the fractions for R and W we get 5/12N=3/8N+24. So (5/12-3/8)N=24. 24 is the lowest common denominator of 8 and 12 so this equation can be written: (10-9)N/24=24, from which N=576. (This means that there are 216 white, 240 red and 120 blue paper clips.)