Water for the Track Meet
The student council must supply water for a 6-hour track meet with 180 athletes. The plan is to provide 1.5 L per athlete plus a 10% reserve. Water is sold only in cases of 24 bottles, each bottle 500 mL, at $4.25 per case. The council has $150. A parent volunteer offers one car; its trunk measures 0.35 m³. Each case measures 40 cm × 27 cm × 24 cm. The council wants to buy all the water in one shopping trip and load it into that car. Before ordering, they ask you to check whether the plan is feasible and, if not, to propose the smallest change that makes it work.
1. How many cases must the council buy to meet the 1.5 L per athlete plus 10% reserve? Show the unit conversions.
Read the worked answer
Total water needed = 180 × 1.5 L = 270 L. Reserve = 10% of 270 = 27 L. Total = 297 L.
Each bottle is 500 mL = 0.5 L, so bottles needed = 297 ÷ 0.5 = 594 bottles.
Cases needed = 594 ÷ 24 = 24.75. Since cases cannot be split, round up to 25 cases. Buying 24 cases gives only 576 bottles = 288 L, which is 9 L short of the 297 L target.
2. Check the budget and the trunk. Does the 25-case plan fit? Show the volume conversion.
Read the worked answer
Cost: 25 × $4.25 = $106.25, which is under the $150 budget.
Volume of one case = 40 cm × 27 cm × 24 cm = 25,920 cm³. Since 1 m³ = 1,000,000 cm³, one case = 0.02592 m³.
Volume of 25 cases = 25 × 0.02592 = 0.648 m³, which is more than the 0.35 m³ trunk. The trunk can hold at most floor(0.35 ÷ 0.02592) = 13 cases (13 × 0.02592 = 0.33696 m³; 14 cases would be 0.36288 m³). So the purchase fits the budget but not one car trip.
3. The council can either make two car trips or rent a van for $45 that holds 0.8 m³. Which option meets all constraints at lower total cost? Justify with numbers.
Read the worked answer
Two trips: split 25 cases into 13 and 12 cases. Each load is under 0.35 m³ (13 cases = 0.33696 m³; 12 cases = 0.31104 m³). Total cost remains $106.25, under $150.
Van: $45 rental plus $106.25 water = $151.25, which is $1.25 over the $150 budget. The van's 0.8 m³ holds 30 cases, so space is fine, but the budget fails.
Lower-cost feasible option: make two car trips. If the school can raise the budget by at least $1.25, the one-trip van option also works; otherwise two trips is the smallest change.