Question: User: 🧠🧠 Spicy: School Trip Cost Challenge A school is planning a trip for 168 students and 12 teachers. Transport Option A • 4 buses • each bus seats 45 people • $186.50 per bus • parking costs $24 per bus • one total toll charge of $18.75 Transport Option B • 5 minibuses • each minibus seats 36 people • $149.80 per minibus • parking costs $16.50 per minibus • no toll charge Other cost • Lunch vouchers cost $7.25 per person for everyone going. Budget • The school has a total budget of $2400. Your tasks Part 1: Write a mathematical model Write an expression for the total cost of Option A and an expression for the total cost of Option B. Part 2: Capacity check Decide whether each option can carry everyone. Part 3: Calculate Find the exact total cost for each valid option. Part 4: Decide and justify • Which option should the school choose? • Is the budget enough? • How much money will be left? • Explain why your answer is reasonable. If you got stuck, do not leave it blank. Show what you can do and write one sentence explaining where you got stuck. top-left: A rectangular table with a central vertical divider and one horizontal divider, forming four sections; the top-left section is labeled Transport Option A, the top-right is Transport Option B, the bottom-left is Other cost, and the bottom-right is Budget.

1. **State the problem:** We need to compare two transport options for a school trip with 168 students and 12 teachers (total $168 + 12 = 180$ people). We will write cost expressions, check capacity, calculate total costs, and decide which option fits the budget best. 2. **Write expressions for total cost:** - Let $n = 180$ be the total number of people. **Option A:** - Number of buses: 4 - Cost per bus: $186.50$ - Parking per bus: $24$ - Toll charge total: $18.75$ - Lunch vouchers per person: $7.25$ Total cost for Option A: $$\text{Cost}_A = 4 \times 186.50 + 4 \times 24 + 18.75 + 180 \times 7.25$$ **Option B:** - Number of minibuses: 5 - Cost per minibus: $149.80$ - Parking per minibus: $16.50$ - No toll charge - Lunch vouchers per person: $7.25$ Total cost for Option B: $$\text{Cost}_B = 5 \times 149.80 + 5 \times 16.50 + 0 + 180 \times 7.25$$ 3. **Capacity check:** - Option A capacity: $4 \times 45 = 180$ seats - Option B capacity: $5 \times 36 = 180$ seats Both options can carry exactly $180$ people, so both are valid. 4. **Calculate total costs:** **Option A:** - Bus cost: $4 \times 186.50 = 746$ - Parking cost: $4 \times 24 = 96$ - Toll charge: $18.75$ - Lunch vouchers: $180 \times 7.25 = 1305$ Sum all: $$746 + 96 + 18.75 + 1305 = 2165.75$$ **Option B:** - Minibus cost: $5 \times 149.80 = 749$ - Parking cost: $5 \times 16.50 = 82.50$ - Toll charge: $0$ - Lunch vouchers: $180 \times 7.25 = 1305$ Sum all: $$749 + 82.50 + 0 + 1305 = 2136.50$$ 5. **Decision and justification:** - Both options fit the capacity exactly. - Option B is cheaper: $2136.50$ vs $2165.75$. - Budget is $2400$, both options are under budget. Money left: - Option A leftover: $2400 - 2165.75 = 234.25$ - Option B leftover: $2400 - 2136.50 = 263.50$ **Conclusion:** Option B is the better choice because it costs less and leaves more money in the budget. Both options can carry everyone, so cost efficiency is the deciding factor. This answer is reasonable because all costs and capacities were carefully calculated and compared to the budget.