Question

math word problem for 7th grade students
the amusement park ticket problem
emma is planning a trip to an amusement park with her friends. the park charges an entrance fee of $8 per person. in addition, each person buys a meal inside the park that costs $5 per meal.
part 1: writing the equation
write an equation using the distributive property to represent the total cost, c, for x number of people.
part 2: filling in the table
complete the table below by substituting values of x (the number of people) into your equation.
number of people (x) total cost (c)
1 ?
2 ?
3 ?
4 ?
5 ?
part 4: solve the equation
if emma has a budget of $100, what is the maximum number of people who can go to the amusement park while staying within the budget?

Explanation:

Step1: Define per-person cost

Per person cost: $\$8 + \$5 = \$13$

Step2: Apply distributive property

Total cost equation: $C = 8x + 5x = (8+5)x = 13x$

Step3: Calculate costs for table

Substitute $x=1$: $C=13(1)=13$
Substitute $x=2$: $C=13(2)=26$
Substitute $x=3$: $C=13(3)=39$
Substitute $x=4$: $C=13(4)=52$
Substitute $x=5$: $C=13(5)=65$

Step4: Solve for max people on budget

Set up inequality: $13x \leq 100$
Solve for $x$: $x \leq \frac{100}{13} \approx 7.69$
Since $x$ must be integer, $x=7$

Answer:

Part 1: $C = (8 + 5)x = 13x$
Part 2:

Number of People (x)	Total Cost (C)
2	26
3	39
4	52
5	65

Part 4: 7 people