The ratio of the number of manufacturing

The ratio of the number of manufacturing industry workers who were unemployed for 5 to 10 weeks to the number of service industry workers who were unemployed for 5 to 10 weeks is closest to which of the following? 5 to 4, 6 to 5, 3 to 2, 5 to 2, 7 to 6

3 Explanations

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Hey,

Thanks for all the video explanations, they've been extremely helpful! However, I do not understand this one; specifically why did you multiply it by 5/4, or how did you know you need to do it?

Thanks in advance and have a great day!

Jan 6, 2016 • Comment

Sam Kinsman

Sure, I'm glad they've helped! :)

We are comparing percentages here, but we aren't comparing percentages of the same initial number. On the left hand side we have a certain percentage of 10 million, and on the right hand side we have a certain percentage of 8 million. That means we can't just compare these percentages directly, since they represent parts of a different whole. Think of it this way: 1% of 10 is not the same as 1% of 8, so we can't just compare the percentages directly.

We need to ask ourselves how much bigger 10 is than 8, and we find that 10 is 5/4ths of 8. Therefore, each single percent of 10 is 5/4ths of each single percent of 8. So if we multiply the percentage on the left hand side by 5/4, we can then compare the two percentages directly.

Jan 8, 2016 • Reply

Jacob Elder

I'm confused. If 8 million is the smaller portion, wouldn't you multiply 8 and it's corresponding percentage by 5/4 to make it equivalent to 10 million? Why would you multiply 10 million by 5/4 if you're trying to make them equivalent? Since 10 million is 5/4 of 8 million, shouldn't 8 million and it's percentage be increased so that they can be compared?

Jan 28, 2016 • Reply

Sam Kinsman

Hi Jacob, I can help! :) If you haven't read it already, I think you might find the comment I posted above helpful. Essentially, we know that 10 million is 5/4ths greater than 8 million, so each single percent of 10 million is 5/4ths of each single percent of 8 million. That's why 10 million's percentage is multiplied by 5/4ths.

Feb 16, 2016 • Reply

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Jacob Elder

So if you were to multiply .26 times 10, it would be 2.6, and if you were to multiply .16 times 8, this would be 1.28. I figured that if you compare 1.28 to 2.6, this could then be the ratio, but it appears that it does not equate to 3:2. Why is that?

Jan 28, 2016 • Comment

Sam Kinsman

I think you meant to multiply .20 by 10, and not .26. (The percentage of unemployment for the manufacturing industry is 20%). This way, you'll get 2.0 and 1.28. When we compare these two numbers, the ratio is very close to 3:2. :)

Feb 16, 2016 • Reply

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Chris Lele