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## Tom, Dick and Harry paid \$120 total for dinner

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.)

Okay, first we need to find the ratio (or percentage) of cash held by Tom and Harry to the total amount:
- We need to find the total cash held to do this so we do: 100 + 60 + 40 = \$200.
- Next we find the ratio of Tom's cash held to the total: 100/200 = 1/2 (or 50%).
- Then we find Harry's ratio: 40/200 = 1/5 (or 20%).
Next we need to use our ratios on the amount spent at dinner to find the amount that Tom and Harry paid:
- First we find how much Tom paid by multiplying the ratio (or percent) by the total amount because the problem told us the ratios are the same: 120*(1/2) = \$60 (you could also do 120*50% = 120*0.5 = \$60).
- Next we find Harry's amount using the same method: 120*(1/5) = \$24 (you could also do 120*20% = 120*0.2 = \$24).
Finally, we need to find the difference between the two: 60 - 24 = \$36.