Question

Elliot has a landscape maintenance business. His monthly expenses are $\backslash (1,100$. If he charges $\backslash )60$per job, how many jobs must he do to earn a profit of at least $\$4,000$a month?

Short answer

He must have to do $85$jobs to earn a profit of at least $\$4,000$.

Step-by-step solution

Step 1. Given information

We have given that Elliot charges $\$60$to do a job. His monthly expenses are of $\$1,100$.

He wants to earn a profit of at least $\$4,000$.

We have to find hoe many jobs he have to to earn a profit of at least $\$4,000$.

Step 2. Convert to an inequality

Let he have to do $n$jobs to earn a profit of at least $\$4,000$.

From given information we have :-

$60$times jobs to done minus $\$1,100$is at least $\$4,000$.

From this statement we have the following inequality :-

localid="1644344642355" $60n-1100\ge 4000$

Step 3. To solve the inequality

Add $1,100$on both sides of the inequality, then we have :-

$$\begin{gathered} 60n-1100+1100\ge 4000+1100 \\ \Rightarrow 60n\ge 5100 \end{gathered}$$

Divide both sides of the inequality by $60$, then we have :-

$$\begin{gathered} \frac{60n}{60}\ge \frac{5100}{60} \\ \Rightarrow n\ge 85 \end{gathered}$$

Step 4. Final Conclusion

We find that $n\ge 85$, where $n$is the number of the jobs to do.

Then we can conclude that :-

He must have to do $85$jobs to earn a profit of at least$\$4,000$.