Middle School Math Quiz: Linear Function Modeling
6 questions · exam conditions
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Linear Function ModelingQuestion 1 of 6

The cost to produce t-shirts is given by C(x)=8x+150C(x) = 8x + 150, where x is the number of t-shirts and C is the cost in dollars. If the company sells each t-shirt for $15, how many t-shirts must be sold to achieve a profit of exactly $200?

45 t-shirts
50 t-shirts
55 t-shirts
60 t-shirts
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Middle School Math Quiz

Middle School Math Quiz: Linear Function Modeling

Practice Linear Function Modeling in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Linear Function Modeling, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

The cost to produce t-shirts is given by C(x)=8x+150C(x) = 8x + 150, where x is the number of t-shirts and C is the cost in dollars. If the company sells each t-shirt for $15, how many t-shirts must be sold to achieve a profit of exactly $200?

  1. 45 t-shirts
  2. 50 t-shirts (correct answer)
  3. 55 t-shirts
  4. 60 t-shirts
Explanation: Revenue = 15x, Cost = 8x + 150. Profit = Revenue - Cost = 15x - (8x + 150) = 7x - 150. Set profit equal to 200: 7x - 150 = 200, so 7x = 350, therefore x = 50. Choice A results from setting profit = 165 instead of 200. Choice C comes from using revenue equation instead of profit. Choice D results from miscalculating 7x = 420.

Question 2

A taxi company charges a flat fee of $3.50 plus $0.75 per mile. If Maria's taxi ride costs $18.25, and she wants to tip the driver 20% of the total fare, what is the total amount Maria will pay including the tip?

  1. $21.90 (correct answer)
  2. $19.65
  3. $22.50
  4. $20.85
Explanation: First, set up the equation: 3.50 + 0.75m = 18.25, where m is miles. Solving: 0.75m = 14.75, so m = 19.67 miles. The fare is $18.25, and 20% tip = 0.20 × 18.25 = $3.65. Total = 18.25 + 3.65 = $21.90. Choice B incorrectly calculates tip as 0.20 × 14.75. Choice C uses 20% of the base fare plus tip incorrectly. Choice D miscalculates the tip percentage.

Question 3

A water tank is being filled at a constant rate. After 15 minutes, the tank contains 180 gallons. After 35 minutes, it contains 300 gallons. If the tank was not empty initially, how many gallons were in the tank when filling began?

  1. 45 gallons
  2. 60 gallons
  3. 75 gallons
  4. 90 gallons (correct answer)
Explanation: The rate is (300 - 180)/(35 - 15) = 120/20 = 6 gallons per minute. Using point (15, 180): initial amount = 180 - 6(15) = 180 - 90 = 90 gallons. Choice A assumes the tank started empty and calculates incorrectly. Choice B uses the wrong time interval. Choice C miscalculates the rate as 4 gallons per minute.

Question 4

A phone plan costs $25 per month plus $0.05 per text message. Another plan costs $35 per month with unlimited texting. After how many text messages in a month would both plans cost the same amount?

  1. 150 messages
  2. 200 messages (correct answer)
  3. 250 messages
  4. 300 messages
Explanation: Set up equation: 25 + 0.05t = 35, where t is number of texts. Solving: 0.05t = 10, so t = 200 messages. Choice A results from solving 25 + 0.05t = 32.50. Choice C comes from using $0.04 per text instead of $0.05. Choice D results from setting up the equation incorrectly as 25 + 0.05t = 40.

Question 5

A swimming pool is being drained at a constant rate. The pool initially contains 8,000 gallons. After 2 hours, it contains 6,800 gallons. At this rate, how many hours after draining began will the pool contain exactly 4,000 gallons?

  1. 6.0 hours
  2. 7.3 hours
  3. 6.7 hours (correct answer)
  4. 8.0 hours
Explanation: This is a linear rate problem where you need to find when the pool will reach a specific amount. When you see constant rate problems, think about finding the rate of change first, then using it to predict future values. Start by calculating the drainage rate. The pool lost 8,000−6,800=1,2008,000 - 6,800 = 1,200 gallons in 2 hours, so the rate is 1,200 gallons2 hours=600\frac{1,200 \text{ gallons}}{2 \text{ hours}} = 600 gallons per hour. Now you can set up an equation. The amount remaining after tt hours is: 8,000−600t=gallons remaining8,000 - 600t = \text{gallons remaining} To find when the pool contains exactly 4,000 gallons: 8,000−600t=4,0008,000 - 600t = 4,000 Solving: 600t=8,000−4,000=4,000600t = 8,000 - 4,000 = 4,000, so t=4,000600=6.67t = \frac{4,000}{600} = 6.67 hours, which rounds to 6.7 hours. Looking at the wrong answers: A) 6.0 hours would leave 8,000−600(6)=4,4008,000 - 600(6) = 4,400 gallons, not 4,000. This might result from rounding the rate incorrectly. B) 7.3 hours would leave 8,000−600(7.3)=3,6208,000 - 600(7.3) = 3,620 gallons, which could come from miscalculating the drainage rate. D) 8.0 hours would leave 8,000−600(8)=3,2008,000 - 600(8) = 3,200 gallons, possibly from using the wrong initial amount or confusing the setup. For constant rate problems, always identify the rate first, then set up your equation carefully. Double-check by substituting your answer back into the original scenario to verify it makes sense.

Question 6

A bicycle rental shop charges $12 for the first hour and $8 for each additional hour. Which linear function represents the total cost C(h) for renting a bicycle for h hours, where h ≥ 1?

  1. C(h)=12+8hC(h) = 12 + 8h
  2. C(h)=8h+12C(h) = 8h + 12
  3. C(h)=8h+4C(h) = 8h + 4 (correct answer)
  4. C(h)=20hC(h) = 20h
Explanation: This question tests your ability to translate a real-world pricing structure into a linear function. When you see "charges X for the first hour and Y for each additional hour," you need to carefully break down what happens at each step. Let's think through the cost structure: For 1 hour, you pay $12. For 2 hours, you pay $12 (first hour) + $8 (second hour) = $20. For 3 hours, you pay $12 + $8 + $8 = $28. Notice the pattern: the total cost equals $12 plus $8 times the number of additional hours. Since h represents total hours rented, the number of additional hours is (h - 1). Therefore: $C(h)=12+8(h−1)=12+8h−8=8h+4C(h) = 12 + 8(h - 1) = 12 + 8h - 8 = 8h + 4 $. This matches answer choice C. Answer A, C(h) = 12 + 8h , incorrectly adds 8foreveryhourincludingthefirst,whichwouldmeanpaying8 for every hour including the first, which would mean paying 12 + 8=8 = 20 for just one hour. Answer B, C(h) = 8h + 12 , makes the same error as A—it's mathematically equivalent but written differently. This would charge 20forthefirsthourinsteadof20 for the first hour instead of 12. Answer D, C(h) = 20h , completely ignores the two-tier pricing structure and assumes a flat $20 per hour rate. Study tip: When dealing with "first unit costs X, additional units cost Y" problems, always identify what represents the additional units. Here, if h is total hours, then additional hours = (h - 1). Build your function step by step from the word problem.