Dividing the profits - Math Central

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Question from Tracy, a student:

I need to know how to come up with the answers to the following problems. I need to be able to show my work. So can you help me on how to come up with the answers to questions like these. Thanks.

Three individuals form a partnership and agree to divide the profits equally. X invests
$9,000, Y invests $7,000, Z invests $4,000. If the profits are $4,800, how much less
does x receive compared to having the profits divided in proportion to the amounts
invested by X, Y, and Z?

In printing an article of 48,000 words, a printer decides to use two sizes of type. Using the
larger type, a printed page contains 1,800 words. Using a smaller type, a page contains
2,400 words. The article is allotted 21 full pages in a magazine. How many pages must be
in smaller type? ___________

thank you

Hi Tracy,

You are instructed to show your work not mine so I am not going to do these problems for you but I will help her you started on the first problem.

If the profit is $\$4,800$ and they split it 3 ways then each of them will get $\$4,800/3 = \$1,600.$

Together they invested $\$9,000 + \$7,000 + \$4,000 = \$20.000.$ The fraction of the investment that came from X is $\large \frac{\$9,000}{\$20,000} = \frac{9}{20}.$ Thus if they divide the profit in proportion to the amount invested than the fraction of the profit coming to X will be $\large \frac{9}{20}.$

I hope this helps,
Penny

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