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Rachel, Adam, Michelle, Hannah, and James are going to the movies. They have [tex]$65 to spend on tickets and snacks. Each movie ticket costs $[/tex]9.50, and each snack item costs $4.50. How many snacks can they buy to split among them?

This problem is modeled by the inequality:
[tex]\[ 5(9.5) + 4.5x \leq 65 \][/tex]
which simplifies to:
[tex]\[ 47.5 + 4.5x \leq 65 \][/tex]

1. The first step in solving the inequality is to subtract 47.5 from both sides:
[tex]\[ 4.5x \leq 65 - 47.5 \][/tex]

2. The second step is to divide both sides by 4.5:
[tex]\[ x \leq \frac{17.5}{4.5} \][/tex]

The five friends will have to split the snacks.

Sagot :

GinnyAnswer
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.
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