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21 April, 15:51

Let's say you plan to start a lawn-mowing business for a little extra money over the

summer. A new lawn-mower costs $450. Between the gas you use and the time is takes to travel (your time is important, after all), you estimate you will incur a cost of approximately $6 per lawn you mow. If you charge $35 for each lawn you mow, how many lawns must you mow before you become profitable?

If you plan on mowing only 3 lawns per day, 5 days per week, over the summer, how

long will it take to make a profit of $2,500? Do you think this is a reasonable goal? Why or why

not?

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Answers (1)
  1. 21 April, 18:00
    0
    Part A.

    You spend $6 per lawn and charge $35 per lawn, so the profit per lawn is $35 - $6 = $29. Let the number of lawns you mow be n. You earn a profit of $29 pewr laun, so you earn a profit of 29n for mowing n lawns.

    29n = 450

    Divide both sides by 29.

    n = 450/29 = 15.517 ...

    You must mow 16 lawns to make profit.

    Part B.

    3 lawns per day for 5 days per week means 15 lawns per week. Since you make a profit of $29 per lawn, you will make a profit of 15 * $29 for 15 lawns in each week. 15 * $29 = $435.

    You want to make $2500 profit, but you must spend $450 on the lawn mower, so you need to earn a total of $2500 + $450 = $2950.

    Let n be the number of weeks. In one week, you make $435 in profit. In n weeks, you make 435n in profit.

    435n = 2950

    Divide both sides by 435.

    n = 6.7816 ...

    If you work for 7 weeks, you will make at least $2500 in profit.

    Since the summer vacation is longer than 7 weeks, it is a reasonable goal, but you must take into account the time it takes to mow three lawns in one day.
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