Class Trip: Balance the Budget
0 / 14Class Trip: Balance the Budget
Use linear equations to check bus, meal, and museum costs.
Check Individual Costs
Solve each equation. Each question is a separate budget check; all money amounts are in dollars.
1.
A bus company charges 75% of its regular price, x, plus a $96 driver fee. The total is $330. Solve 0.75x + 96 = 330.
The regular bus price is $.
2.
A meal package costs 0.6x dollars for food, 0.25x dollars for a drink, and $1.50 for packaging. The total is $10. Solve 0.6x + 0.25x + 1.50 = 10.
x =
3.
A museum adds a $3 activity fee to its regular ticket price, x. A school pays 2/3 of that combined amount, or $10. Solve (2/3)(x + 3) = 10.
The regular ticket price is $.
4.
A meal voucher calculation gives 0.8(x + 5) + 2 = 18. Which value solves the equation?
5.
Two museum ticket offers have the same cost when (3/4)x + 6 = (1/2)x + 11. Find x.
x =
Audit the Calculations
Distribute carefully and combine like terms. Show steps that preserve equality.
6.
A trip budget worksheet includes 0.5(3x + 12) + 0.25(x − 4) = 40. Which equation is equivalent after distributing and combining like terms?
7.
A meal refund check gives 18 − 0.4(x + 5) = 0.6x + 7. Solve for x.
x =
8.
A ticket-cost allocation uses the equation (x + 6)/4 + (x − 2)/3 = 9. Find x.
x =
9.
Two bus quote calculations agree when 0.9(x − 10) + 0.3x = 0.6(x + 5) + 24. Solve for x.
x =
10.
Priya solves a budget equation, (x + 8)/3 + x/2 = 16. She says she multiplied every term by 6 and writes 2(x + 8) + x = 96. Explain what she missed. Write the corrected equation and solve for x.
Make Budget Decisions
Write and solve an equation for each situation. Report the quantity requested, not just the variable.
11.
For one trip, 24 students each pay $24. Meals cost $144, and museum tickets cost $192. A grant pays 1/4 of the bus cost. The students' payments cover exactly the remaining bus cost plus all meals and tickets. What is the full bus cost?
The full bus cost is $.
12.
Two meal providers use the same base price, x dollars. Their final prices are shown below. At what final price per meal do the offers cost the same?
| Provider | Final price ($) |
|---|---|
| Fresh Lunch | 0.85(x + 2) |
| Ready Meals | 0.65x + 4.10 |
Each offer costs $ per meal.
13.
A museum sells 30 student tickets at a regular price of x dollars each. It also sells 4 adult tickets at (x + 3) dollars each. The museum charges the school 3/4 of the combined ticket cost. The school pays $264. What is the regular student ticket price?
14.
A class plans meals for 28 students. Each meal's listed price is x dollars, and a group discount reduces that price by $1.50 per meal. The bus costs $210. Museum tickets cost 1/2 of the listed meal price per student. These are the only expenses, and their total is $672. What is the discounted price of one meal?
The discounted meal price is $.