Math problem set Grade 7 Math
Brackenmoor Retention Basin: A Budget and Percent Problem Set
Eight problems where students apply a bulk discount, sales tax, and an installation fee to a stormwater basin materials budget and check it against a total.
Objectives
- Students will calculate a percent discount and apply it to a materials cost.
- Students will calculate sales tax and an installation fee, then combine multiple dollar amounts to check a project against a budget.
Vocabulary
Key words: discount, sales tax, installation fee, budget
Teacher overview
The fictional town of Brackenmoor is building a stormwater retention basin to hold runoff from a new stretch of road, and the engineering team assigned to the project has been given a materials budget and a set of supplier quotes. This problem set walks students through the same math a project engineer would use: applying a bulk-order discount to gravel, adding sales tax to a liner, adding an installation fee to a pump, and checking whether the combined cost fits inside the town's stated budget. A common misconception in this math is treating a percent decrease and a percent increase as if they cancel out or can be combined into a single step, rather than calculating each one separately, in order, against the correct starting amount.
Problems
For this fictional scenario, Brackenmoor has budgeted $18,000 for the basin's materials and installation. Use these facts for all problems:
- Gravel: 40 tons at $150 per ton, before any discount.
- The gravel supplier offers 10 percent off any order over 30 tons.
- Liner: $6,200 before tax. Local sales tax is 6 percent.
- Pump system: $4,500 before fees, plus a 15 percent installation fee.
Find the gravel's cost before the discount is applied.
The order qualifies for the supplier's 10 percent discount. Find the discount amount, then find the gravel's discounted cost.
Find the 6 percent sales tax on the liner, then find the liner's total cost including tax.
Find the combined cost of the discounted gravel (problem 2) and the liner with tax (problem 3).
Brackenmoor's total materials budget is $18,000. Using your answer from problem 4, how much of the budget remains after gravel and liner are purchased?
Find the 15 percent installation fee on the pump system, then find the pump's total cost including the fee.
Compare the pump's total cost (problem 6) to the budget remaining after gravel and liner (problem 5). Is there enough remaining budget to cover the pump? By how much money is the project over or under budget?
Challenge. Suppose the gravel supplier had offered only a 5 percent discount instead of 10 percent. How much more would Brackenmoor pay for gravel under this smaller discount, and would the town still have enough total budget to cover gravel, liner, and pump together?
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Answer Key
Answer: $6,000. 40 tons × $150/ton = $6,000.
Answer: $5,400. Discount: 10% of $6,000 = $600. Discounted cost: $6,000 − $600 = $5,400.
Answer: $6,572. Tax: 6% of $6,200 = $372. Total: $6,200 + $372 = $6,572.
Answer: $11,972. $5,400 (gravel) + $6,572 (liner) = $11,972.
Answer: $6,028. $18,000 − $11,972 = $6,028 remaining.
Answer: $5,175. Fee: 15% of $4,500 = $675. Total: $4,500 + $675 = $5,175.
Answer: Yes, $853 under budget. $6,028 (remaining) − $5,175 (pump total) = $853 left over after all three purchases, so the project stays within its $18,000 budget.
Answer: $300 more, and the project would still fit the budget. At a 5% discount, the discount amount is 5% of $6,000 = $300, so the discounted gravel cost is $6,000 − $300 = $5,700, which is $300 more than the original $5,400. Recalculating the total: $5,700 (gravel) + $6,572 (liner) + $5,175 (pump) = $17,447, which is still under the $18,000 budget, with $553 to spare.
Differentiation
Support
For this fictional Brackenmoor scenario, provide the discount, tax, and fee calculations already set up as fill-in equations (for example, "10% of $6,000 = ___" and "$6,000 − ___ = ___") so students complete one operation at a time. Allow a calculator for every problem.
Extension
Ask students to find the single combined percent discount that the gravel supplier would need to offer to bring the fictional project's total cost (gravel, liner, and pump, all at their original problem 1, 3, and 6 costs) down to exactly $17,000, and to show the calculation that supports their answer.
ELL supports
Provide a printed reference card defining "discount," "sales tax," and "installation fee" in plain language, each paired with a simple icon (a price tag with a percent sign, a receipt, a tool). Allow students to show their work using labeled boxes for each step instead of full sentences.