Let's solve the problem step-by-step:
1. Understand the problem and define the variables:
- Total money available: \[tex]$65
- Cost of each movie ticket: \$[/tex]9.50
- Cost of each snack item: \[tex]$4.50
- Number of people: 5
2. Calculate the total cost of the movie tickets for all 5 people:
\[
\text{Total ticket cost} = 5 \times 9.5 = \$[/tex]47.50
\]
3. Determine the remaining money after buying the tickets:
[tex]\[
\text{Remaining money} = 65 - 47.5 = \$17.50
\][/tex]
4. Formulate the inequality that models the situation:
The inequality [tex]\(5 \times 9.5 + 4.5x \leq 65\)[/tex] simplifies to:
[tex]\[
47.5 + 4.5x \leq 65
\][/tex]
5. Solve the inequality step by step:
The first step in solving the inequality is to subtract the total ticket cost from the total money:
[tex]\[
4.5x \leq 65 - 47.5
\][/tex]
Simplifying, we get:
[tex]\[
4.5x \leq 17.5
\][/tex]
The second step is to solve for [tex]\(x\)[/tex] by dividing both sides by the cost of one snack (\$4.50 per snack):
[tex]\[
x \leq \frac{17.5}{4.5}
\][/tex]
Evaluating this gives approximately:
[tex]\[
x \leq 3.8889
\][/tex]
6. Determine the maximum number of snacks they can buy:
Since the number of snacks must be a whole number, we take the integer part of the result:
[tex]\[
x \leq 3
\][/tex]
Therefore, the five friends can buy 3 snacks to split among them.
