Seedling Order with a Loss Rate and Budget Limit
Ms. Doucet's Grade 6 garden club has $300.00 for a spring project. The club spends 2/5 of the money on lumber. It then spends 25% of the money remaining on soil. Seedlings are sold in trays of 18 for $12.60 per tray, plus 8% tax on the seedling order. The club wants 150 healthy plants. The supplier warns that about 1 in 9 seedlings will not survive transplanting, so extra seedlings must be bought. Jalen says, 'Nine trays are enough because 9 × 18 = 162, and 162 is more than 150.' The club must buy whole trays, pay the tax, and cannot spend more than the money left after lumber and soil. They need to place the order tomorrow and have no extra fundraising money yet.
1. How many trays must the club buy to end up with at least 150 healthy plants? Show the calculation and decide whether the remaining money is enough.
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After lumber: $300.00 − (2/5 × $300.00) = $300.00 − $120.00 = $180.00. After soil: 25% of $180.00 = $45.00, so $180.00 − $45.00 = $135.00 remains. Each tray has 18 seedlings, but 1 in 9 do not survive, so 8/9 survive. Healthy plants per tray = 18 × 8/9 = 16. To get at least 150 healthy plants, divide 150 by 16: 150 ÷ 16 = 9.375. Whole trays are required, so round up to 10 trays. Cost before tax = 10 × $12.60 = $126.00. Tax = 8% × $126.00 = $10.08. Total = $136.08. The club has $135.00, so it is short by $1.08. Ten trays are the minimum; nine would give only 144 healthy plants.
2. Jalen calculates 9 trays because 9 × 18 = 162, which is more than 150. Explain why his reasoning is incomplete and what the correct interpretation of the loss rate is.
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Jalen is comparing seedlings planted with healthy plants. Nine trays contain 9 × 18 = 162 seedlings, but the loss rate means only 8/9 of them are expected to survive. 162 × 8/9 = 144 healthy plants, which is 6 short of 150. The 1-in-9 loss is not a reason to buy one extra seedling; it applies to every tray, so the class must plan for 16 healthy plants per tray, not 18. Dividing 150 by 16 and rounding up gives 10 trays. Ten trays contain 180 seedlings; after losing 20, about 160 healthy plants remain, which is 10 more than the target. The extra plants are a buffer because the loss rate is an estimate, not a guarantee.
3. The club cannot spend more than $135. Propose one change that would let them buy 10 trays without reducing the number of healthy plants below 150. Show the math and one trade-off.
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One realistic change is to ask the school office to cover the 8% tax on the seedling order, $10.08, from its supplies budget. The club would then pay only $126.00 for 10 trays, which is within the $135.00 remaining and leaves $9.00. This keeps the plan at 10 trays and about 160 expected healthy plants, so it does not reduce the number below 150. The trade-off is that the office must use money intended for other supplies, and the club should explain why the request is one-time. A second option is a bottle-return drive to raise at least $1.08; raising $2.00 would cover the shortfall and leave a small buffer, but it takes time before the order is due.