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How do you solve a proportional and non proportional relationship question?

Mathematics
Tutor: None Selected Time limit: 1 Day

for instance: 

in July, a paleontologist found 368 fossils at a dig. In August, she found 14 fossils a day.

Is the total number of fossils found during July and August proportional to the number of days the paleontologist spent looking for fossils in August?

Thought this is for my homework, I am not looking for direct answers. I would just like an explanation on how to do these type of questions and the concept.

Thank you!

Mar 19th, 2015

Yes, you're on the right track.

In July, the paleontologist found 368 fossils. There are 31 days in July. So 368/31 = 11.87 fossils per day. That's the PROPORTIONALITY COEFFICIENT,  which means, if you write an equation where y equals the total number of fossils found in a month, then

y = 11.87x   where x is the number of days digging.

In August, she found 14 fossils per day. That's MORE than the month before. So, the equation for August becomes

y = 14x

August also has 31 days, so we expect she will find

y = 14(31) = 434 fossils.

Hope that helps.

Mar 19th, 2015

Thank you so much for replying. It slipped my mind to put this in the question but we need to find if it is or isn't proportional. I would be very thankful if you could explain how to do that. Thanks!

Mar 19th, 2015

Yes, it is proportional because the number of fossils found and the number of days digging are directly related and proportional, that is to say, the more days she digs the more fossils she finds.

Mar 19th, 2015

Hold on a moment. After reading the question in the problem you wrote I want to change my answer. It asks if the number of fossils found in JULY and AUGUST, both months together, is proportional to the number of days in August ALONE. Then the answer is no, because the fossils found in July took 31 days, and the number of fossils in August took 31 days, for a total of 62 days.

Mar 19th, 2015

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Mar 19th, 2015
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Mar 19th, 2015
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