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# Word Problems/Ratios

Question
Hello:

I am interested in learning an alternative solution to the following:

Two people share \$49,500 in a ratio of 8 to 7.  How much each person get?

Solution:

8 X 1/15 X \$49,500 = \$26,400

7 X 1/15 X \$49,500 = \$23,100

Do you know of a somewhat simple solution that does not use 1/15 to determine the answers?

The ratio is based on 15, so using 8/15 and 7/15 is the most straightforward way to calculate each share.

You can certainly convert the denominators to some other number. For example,
8/15 = 16/30, 24/45, 32/60, ...

However, unless the new denominator is a multiple of 15, the conversion itself requires division by 15. For example, to use a denominator of 100, you would multiply both numerator and denominator by (100/15):

8/15 = [8·(100/15)]/[15·(100/15)] = 53.333.../100

so you still have to divide by 15 (twice!) and end up with an even more unwieldy fraction.
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thanks for the reply and explanation!

Word Problems

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#### Janet Yang

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Word problems are my favorite type of math questions! I would not feel comfortable answering questions that require specialized knowledge (Physics, Statistics, etc.) because I have not studied these in depth.

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I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

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