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?
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.
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?
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.
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?
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. :)
3 Explanations