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Who Has the Best Job?


Alignments to Content Standards: 8.EE.B.5

Task

Kell works at an after-school program at an elementary school. The table below shows how much money he earned every day last week.

Monday Wednesday Friday
Time worked 1.5 hours 2.5 hours 4 hours
Money earned \$12.60 \$21.00 \$33.60

Mariko has a job mowing lawns that pays \$7 per hour.

  1. Who would make more money for working 10 hours? Explain or show work.

  2. Draw a graph that represents $y$, the amount of money Kell would make for working $x$ hours, assuming he made the same hourly rate he was making last week.

  3. Using the same coordinate axes, draw a graph that represents $y$, the amount of money Mariko would make for working $x$ hours.

  4. How can you see who makes more per hour just by looking at the graphs? Explain.

Solution

  1. Mariko would make $7\times 10 = 70$ dollars for working 10 hours. Kell's hourly rate can be found by dividing the money earned by the hours worked each day.

      Monday Wednesday Friday
    Time worked 1.5 hours 2.5 hours 4 hours
    Money earned \$12.60 \$21.00 \$33.60
    Pay rate \$8.40 per hour \$8.40 per hour \$8.40 per hour
    If Kell works for 10 hours at this same rate, he will earn $8.4\times 10 = 84$ dollars. So Kell will earn more money for working 10 hours.

    Alternatively, we could reason proportionally without computing the unit rate.  Since Mariko earned \$21.00 for 2.5 hours, she will earn four times as much for working four times as long ($10=4\times 2.5$), for a total of $4\times \$21=\$84$.

  2. See the figure below.

  3. See the figure below.

  4. You can see that Kell will make more per hour if you look at the points on the graph where $x=1$ since this will tell you how much money each person will make for working 1 hour. You can also compare the slopes of the two graphs, which are equal to the hourly rates. See the figure below.

1_63805eb69b376a6441aa220978c20414

Connie says:

about 3 years

Problem a) could be reasoned by looking at the table and noting that 2.5 hours could be doubled to 5 hours then double again for 10 hours. Then \$21.00 can be doubled twice or 21 $\times$ 4 = \$84.00. Let's keep all ways of reasoning open to students.

For problem d) students are asked to answer 'by looking at the graph'. They may answer the question without naming specific points. By looking at the graph, for every time period that Kell works she makes more money than Mariko. Students could then verify by naming some points and noting the unit rates.

Cam says:

about 3 years

Thanks for these comments. I completely agree on (a), and have added a line in the solution providing yours as an alternative. For (d), I agree as well, though the question specifically asks if students can deduce the comparison of unit rates just by looking at the graph.