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Question: Part time students take $60\%\ (6/10)$ of the course load of full time students, and there are $1000$ part time students. How many full time equivalent students are there?

The answer is $(6/10)×1000=600$, but I cannot figure out what the numerator/denominator units of the $60\%$ figure are. If $1000$ units is "part time students", the denominator $(10)$ must be "part time students", but I cannot then figure out what the $6$ would be.

Help? Thanks!

Alejandro Tolcachier
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findingmyway
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1 Answers1

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The key is to interpret the ratio as the comparison (in some way) of full-time students to part-time ones. Since you're told that (the load of) 10 part-time students is equal to (the load of) 6 full-time students, your ratio is

60% = 6 full-time students / 10 part-time students

SBRJCT
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  • I appreciate the response! I understand what you're saying, but I'm having trouble getting to 6 full time students/10 part-time students. Can you explain this a little more? Thanks! – findingmyway Aug 21 '20 at 04:40
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    Here’s an analogy: replace “full-time students” with $ and “part-time students” with a fictitious currency with symbol &. Then you’re told that &10 has the value of $6 (& isn’t worth as much as $), or, in other words, $6=&10. Therefore, 1 = $6/&10 and so &1000 = ($6/&10)*&1000 = $600. – SBRJCT Aug 21 '20 at 04:56
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    Right. Or said otherwise, .6 full time students =1 part time student, thus .6/1 Thanks again! – findingmyway Aug 21 '20 at 05:01