Splitting a Supply Budget
A student club has a budget of $240 for an event. They must buy plates and cups. Plates come in packs of 20 for $6 each. Cups come in packs of 25 for $5 each. They expect 150 guests and want at least one plate and one cup per guest, but they may not need extras. They also want to keep at least $30 of the budget unspent as a reserve. Packs cannot be split, and they cannot buy partial packs. A member suggests buying 8 packs of plates and 6 packs of cups.
1. Does the member's suggestion meet the per-guest requirement and the reserve requirement? Show the arithmetic.
Read the worked answer
8 packs of plates = 8 × 20 = 160 plates, costing 8 × $6 = $48. 6 packs of cups = 6 × 25 = 150 cups, costing 6 × $5 = $30. Total spent = $48 + $30 = $78. Plates (160) and cups (150) both cover 150 guests, so the per-guest requirement is met. Money left = $240 − $78 = $162, which is well above the $30 reserve. So the suggestion satisfies both requirements, though it spends far less than allowed and leaves a large surplus.
2. Find the least expensive purchase that still covers 150 guests of both items, and state whether it respects the $30 reserve.
Read the worked answer
For plates, 150 ÷ 20 = 7.5, so she needs 8 packs (160 plates), costing $48. For cups, 150 ÷ 25 = exactly 6, so 6 packs (150 cups), costing $30. Minimum total = $48 + $30 = $78. Since $240 − $78 = $162 remains, the reserve of $30 is easily respected. Note the reasoning trap: you cannot round 7.5 packs down to 7, because 7 packs give only 140 plates and would leave 10 guests without a plate. Rounding up on the indivisible item is what makes the answer correct.