Multiple methods
There are often several ways to solve a problem.
Explore several methods of solving the following problem.
Jenny is the director of a holiday camp for kids. Each year she needs to employ counsellors for the camp. The number of counsellors she employs is directly proportional to the number of kids who come to the camp. Last year there were 320 kids and 20 counsellors. If there are only 240 kids coming this year, how many counsellors should she employ?
Use the method in the previous section, Graphing in GeoGebra, to solve the problem.
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You will need to plot a point that corresponds to the number of kids and counsellors last year.
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Remember that every graph of direct proportionality passes through the origin.
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Read the coordinates of the point on the graph that corresponds to 240 kids coming to the camp.
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Complete this sentence using a fraction: To get from 320 to 240 we multiply by ___.
(Hint: What fraction is 240 of 320?) -
Since the quantities are in direct proportion we can multiply 20 by the same fraction to get the answer.
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The ratio of kids to counsellors is 320:20. Simplify this ratio.
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Your simplified ratio will tell you the number of kids that are allocated to a single counsellor.
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Use your simplified ratio to find the number of counsellors that would be needed for 240 kids.
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Last year there were 320 kids and 20 counsellors. What is the constant of proportionality between kids and counsellors?
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Let c be the number of counsellors and k be the number of kids. Write an equation relating c to k.
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Use your equation to find the number of counsellors that would be needed for 240 kids.