Question

Daniel wants to surprise his girlfriend with a birthday party at her favorite restaurant. It will cost$\backslash (42.75$per person for dinner, including tip and tax. His budget for the party is $\backslash )500$. What is the maximum number of people Daniel can have at the party?

Short answer

Daniel can invite maximum $11$persons at the party.

Step-by-step solution

Step 1. Given Information

The cost of dinner of per person at hotel is $\$42.75$.

Daniel arranges a party at hotel and his budget is $\$500$.

We have to find that how many persons he can invite at the party.

Step 2. Convert to an inequality

Let he can invite $n$peoples at the party.

The cost of per person is$\$42.75$ and his budget is role="math" localid="1645627262248" $\$500$.

Then by using this information, we have the following inequality :-

$42.75n\le 500$.

Step 3. Solve the inequality

Divide both sides of inequality by $42.75$, then we have :-

role="math" localid="1645627383448" $$\begin{gathered} \frac{42.75n}{42.75}\le \frac{500}{42.75} \\ \Rightarrow n\le 11.69 \end{gathered}$$

As $n$is number of peoples, so it must be whole number.

Then round it to $11$.

Then we have :-

$n\le 11$.

Step 4. Final Conclusion

As we find that :-

$n\le 11$.

So we can conclude that Daniel can invite maximum$11$ peoples at his party.