Sure, let's solve this step-by-step.
First, let's determine the total cost of the movie tickets for all five people.
1. Calculate the total ticket cost:
Each movie ticket costs \[tex]$9.50, and there are 5 people.
\[
\text{Total ticket cost} = 9.50 \times 5 = 47.50
\]
So, the total cost for all the tickets is \$[/tex]47.50.
2. Set up and simplify the inequality for snack costs:
We need to account for the cost of snacks within the remaining money. Let [tex]\( x \)[/tex] represent the number of snacks.
The inequality [tex]\( 47.5 + 4.5x \leq 65 \)[/tex] represents the total cost.
Subtract the total ticket cost from the total amount of money available:
[tex]\[
65 - 47.50 = 17.50
\][/tex]
So, we rewrite the inequality as:
[tex]\[
4.5x \leq 17.50
\][/tex]
3. Solve for [tex]\( x \)[/tex], the number of snacks:
Divide both sides by 4.5 to isolate [tex]\( x \)[/tex]:
[tex]\[
x \leq \frac{17.50}{4.50} \approx 3.888888888888889
\][/tex]
So, [tex]\( x \approx 3.89 \)[/tex].
This means the maximum number of snacks they can afford is approximately 3.89. Since they cannot buy a fraction of a snack, they can buy 3 snacks and will have a bit of money left over.
Therefore, the friends can buy 3 snacks to share among them.
