Splitting a Catering Budget
A student club has a catering budget of $480 for an event with 60 guests. The caterer charges a flat delivery fee of $45 and a per-person meal cost of $7.25. The club also wants to buy 60 bottled waters at $1.10 each, but only if the total stays within budget. A local store offers a 15% discount on bottled water when at least 48 bottles are purchased. The club treasurer estimates the total as 60 times $7.25 plus $45 plus 60 times $1.10, and concludes the club is over budget by a small amount. The club must decide whether to buy the water, reduce the guest count, or drop the water entirely.
1. Calculate the actual total cost including the water discount, and determine whether the club stays within the $480 budget.
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Meals: 60 times $7.25 equals $435. Delivery: $45. Water before discount: 60 times $1.10 equals $66. The discount applies because 60 is at least 48: 15% of $66 is $9.90, so the water costs $66 minus $9.90, or $56.10. Total: $435 plus $45 plus $56.10 equals $536.10. That exceeds $480 by $56.10. The treasurer's estimate omitted the discount and therefore overstated the water cost, but the club is still over budget. The correct conclusion is that the club cannot afford the water as planned and must change something.
2. The club wants to keep all 60 guests and still buy water. Determine the largest per-person meal cost that keeps the total at or under $480, assuming delivery and discounted water costs stay the same.
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Start with the fixed costs: delivery $45 plus discounted water $56.10 equals $101.10. The remaining money for meals is $480 minus $101.10, or $378.90. Divide by 60 guests: $378.90 divided by 60 equals $6.315 per person. Since meal prices are usually given to the cent, the club needs a per-person cost of at most $6.31 to stay under budget, with $6.32 pushing the total slightly over. This shows the club would need a price reduction of about $0.94 per person from the current $7.25, which is a substantial cut. Reducing the guest count or dropping the water may be more realistic alternatives.