Percent Discount Worksheet

If you're picturing a worksheet where students calculate 15% off a price and move on, this activity asks for more than that. It has students write the discount as a function first, then use that function to answer a real question — because a percent discount only tells you the real cost once you know exactly what else is being added or subtracted.

The clearest example is Part 1. A student named Charlotte finds a 15%-off deal on a home gym, but the fine print requires a $139.95 subscription fee to unlock it. Students write a function for the final before-tax cost that accounts for both the percent discount and the hidden fee, then evaluate it for a real product to decide whether the deal is actually worth it. It's a percent discount problem with a catch, which is closer to how real discounts usually work than a clean 15%-off calculation.

Part 3 is the most direct percent-discount problem in the set. A student named José is choosing between a flat $350 rebate and a 3.5% discount on a used car, and has to write a function for each option before deciding which one actually saves more money once he finds a specific car. Comparing a flat rebate against a percentage discount, as functions of price, is exactly the kind of reasoning a percent discount worksheet should build.

Part 2 is a different kind of problem: two part-time jobs with different hourly rates, travel costs, and tax withholding, worked out as gross-pay and net-pay functions. There's no percent discount in it — it's here because it uses the same function-writing skill as Parts 1 and 3, just applied to wages instead of prices.

One thing worth flagging: the activity's own header describes it as covering compound interest. It doesn't. There's no compounding math anywhere in these three parts. What it actually teaches is the algebra underneath a percent discount — turning a percentage off, with or without a hidden fee, into a function you can evaluate for any starting price.

This activity is from Module 14 of the Rapunzl curriculum, Financial Equations.

Writing Financial Functions

In this activity, students will learn about writing financial functions, including how to model compound interest and calculate present and future values of different financial transactions. By the end of this exercise, students will be able to apply their knowledge of financial functions to real-world scenarios.

PART 1

Charlotte has been saving up to buy a home gym so she can work out at home without having to pay for a gym membership or worry about travel when the weather is bad (she lives in Minnesota where it snows frequently). One day, she sees an ad for a 15% off sale at a fitness equipment store and decides it’s a great time to buy the home gym! She notices the fine print says that to get the 15% off the home gym, she has to pay $139.95 up front for a 6-month subscription to a workout channel, which holds no value to her.

1. Using function notation, write an expression for the final before-tax cost, f(x), of the purchase based on the initial price, x, of the home gym equipment with this deal.
2. She was considering purchasing the AwesomeFlex3000 for $889. Using your function from question 1, what would Charlotte be Charlotte’s before-tax cost with the deal? Is it worth it for her to pay for the subscription to get 15% off? Explain your answer.
3. What is the domain and range of f(x) if the AwesomeFlex is the cheapest option at the store?
4. The store offers a similar deal if you purchase the $139.95 workouts but with a 20% off discount instead of 15% for purchases over $1000. The home gym she’d really like, the Shredmaster5000, costs $1199 before-tax. Write a new function, g(x) for this second deal and calculate the before-tax cost of the Shredmaster5000.
5. If Charlotte lives in Minnesota where sales tax is 6.875% applied at the end of a purchase, what is the domain and range for g(x), including tax, if the ShredMaster is the cheapest system that qualifies for the second deal?

PART 2

Davis is trying to decide between two part time jobs on Saturdays. He could make $16.25 per hour working at the city’s ice arena, but getting to work and back would cost him $7.50 round trip for travel. His other option is to work as a dog walker in his neighborhood for $12.50 per hour but he can ride his bike or walk there for free. He estimates he could work up to 7 hours at the arena but up to 10 hours walking dogs. He always works at least 1 hour if he goes to the arena.

1. Write two different functions that represent Davis’s gross wages, where h is the number of hours Davis works per week, a(h) is his gross wages at the ice arena minus travel expenses, and d(h) is his gross wages from walking dogs.
2. State the domain and range for each function.
3. If Davis works 1 hour, what would be his gross pay at each job? What if he worked 6 hours?
4. Davis wants to know what his net pay, also called take-home pay, is going to be. Assume that 10.5% of just his paycheck, not his travel expenses, is withheld for taxes at the arena. Because dog walking is a self-employed activity, Davis estimates he needs to set aside 18% of his income for taxes. Modify your functions from question 1 to model net pay including these tax withholdings.
5. State the domain and range for each of these new functions.

PART 3: Rebates and Discounts

José is trying to purchase a used car that he has been saving up for. When he gets to the dealership, the car salesperson tells him that there are two deals they have going on that he can choose between. One is a $350 rebate taken off the price of the vehicle, or 3.5% off the listed price.

1. Write two different expressions that represent the total cost of the vehicle with the rebate r(x) or with the percent discount p(x) as a function of the price of the vehicle, x.
2. The salesperson asks if he knows which he wants to choose before he’s even found a car. Why might José have trouble answering this question? What information would help him answer?
3. He searches the lot and finally finds a nice, modest Toyota Corolla listed at $7800. Which deal should José choose, and what will be his total cost?

Teacher Notes

Part 1 is where most of the friction happens. Students want to subtract 15% and stop there, without noticing the $139.95 subscription fee has to be added back into the cost before the deal makes sense one way or the other. Question 3's domain-and-range ask trips students up too, since they need to reason about what values of x are realistic for a store's cheapest item, not just what's mathematically possible.

Part 3 works well as the section to grade closely, since it's a direct competition between a flat rebate and a percent discount and the answer depends entirely on the price of the car. Push students to explain why the better deal changes (or doesn't) as the price goes up — that's the real percent-discount insight underneath the arithmetic.

Part 2 is the most demanding section because it stacks two functions, then asks students to modify both again for taxes. Keep gross pay and net pay clearly separated on the board, since students often conflate the two and lose track of which function they're editing. It's good practice with the same function-writing skill, even though it isn't a discount problem.

The answer key for this worksheet, along with the rest of the activities in this unit, is in the Rapunzl teacher portal.

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