Question

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?

Answer 1

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.

Answer 2

Your profit per lawn is
`payed \minus cost` which is
`35 \minus 6 = 29`.

If you want to be profitable, you must earn more than the cost of the lawn mower. Each mowing you earn 29$. We must divide using the formula
`cost /ide profit = times` where times is the amount of times you must mow lawns to be profitable. We get
`450 /ide 29 = 15.51...`, but you can't only mow parts of a lawn! Therefore, you must mow 16 lawns to be profitable.

Your second part depends on how many weeks are in the summer.

But the answer would look like $435 per week earned, and -$450 one time cost for the lawnmower.