Question

Rameen’s heating bill is $\backslash (5.42$per month plus $\backslash )1.08$per therm. How many therms can Rameen use if he wants his heating bill to be a maximum of $\$87.50$.

Short answer

Rameen can use maximum $76$therms if he wants his heating bill to a maximum of $\$87.50$.

Step-by-step solution

Step 1. Given information

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 $\$87.50$.

Step 2. Convert to an inequality

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 :-

$5.42+1.08n\le 87.50$.

Step 3. Solve the inequality

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

$$\begin{gathered} 5.42+1.08n-5.42\le 87.50-5.42 \\ \Rightarrow 1.08n\le 82.08 \end{gathered}$$

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

$$\begin{gathered} \frac{1.08n}{1.08}\le \frac{82.08}{1.08} \\ \Rightarrow n\le 76 \end{gathered}$$

Step 4. Final Conclusion

We find that :-

$n\le 76$, 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 $\$87.50$.