Question

You can spend no more than $\$100$ on a party you are hosting. The cost per guest is $\$8$.
(A). Write and solve an inequality that represents the numbers of guests you can invite to the party.
(B). What is the greatest number of guests that you can invite to the party? Explain your reasoning.

Answer 1

Step 1 : Given in the question

Total money to spend on hosting party $=\$100$

Cost per guest is $=\$8$

Step 2 : Solve the inequality :

Let the number of invitations for party $=x$

Then total cost of x guests is $=8x$

Then according to given condition given in question we have inequality:

$$\begin{gathered} \Rightarrow 8x<100 \\ \Rightarrow x<\frac{100}{8} \\ \Rightarrow x<12.5 \end{gathered}$$

(A) Solution : Hence, we can invite $12$guests to the party.

Step 3 : Calculate maximum number of guests

As we calculated the inequality as:

$x<12.5$

(B) Solution : Hence, The greatest number of guests that you can invite to the party is $13$.