91Ó°ÊÓ

We have given that heating bill is $\$5.42$per month plus $\$1.08$per therm

Rameen wants his heating bill to be maximum at $\$87.50$.

We have find that how many therms he can use so that the maximum heating bill will be $\$87.50$.

Let he can use $n$therms per month so that his heating bill to be maximum at $\$87.50$.

Also we have the heating bill is $\$5.42$per month plus $\$1.08$times used therms.

From this statement we have the following inequality :-

$5.42+1.08n≤87.50$.

Subtract $5.42$from both sides of the inequality, then we have :-

$$\begin{gathered} 5.42+1.08n-5.42≤87.50-5.42 \\ ⇒1.08n≤82.08 \end{gathered}$$

Now divide both sides by $1.08$, then we have :-

$$\begin{gathered} \frac{1.08n}{1.08}≤\frac{82.08}{1.08} \\ ⇒n≤76 \end{gathered}$$

We find that :-

$n≤76$, where $n$is the number of used therms.

So we can conclude that :-

He can use maximum $76$therms per month if he wants his heating bill to be maximum at $\$87.50$.