If Tom had $100, Dick had $60 and Harry had $40 if the ratio of cash held to cash paid was the same. What was the difference between Tom and Harry's contribution?

Hi, Laura.

Since the ratio of cash held to cash paid is the same, then the ratio of Tom's money held to Dick's money held to Harry's money held is the same as the ratios they paid. The ratio of cash held is 100:60:40 which simplifies to 10:6:4 or 5:3:2.

The ratio of cash paid is the same, so the amounts paid by each can be represented as 5x + 3x + 2x = 120. Solving gives us x=12. We can use that to determine the amount paid by each man.

Tom paid 5 * 12 or $60. Harry paid 2* 12 or $24. The difference is $36. (The difference is also equal to the amount paid by Dick.)