Word Problems
Learning Objectives
In this lesson, you will:
- Translate real-world scenarios into function notation
- Interpret function inputs and outputs in context
- Use functions to model and solve practical problems
- Connect function behavior to real situations
Practice Quiz
Work through these 10 problems. Click each question to reveal the answer and explanation.
Question 1: A taxi charges $3 plus $2 per mile. If C(m) represents the cost for m miles, write the function and find C(7).
Answer: C(m) = 2m + 3; C(7) = $17
Solution: C(m) = 2m + 3. C(7) = 2(7) + 3 = 14 + 3 = 17 dollars.
Question 2: A pool drains at 50 gallons per hour. If it starts with 2000 gallons, write W(t) for water remaining after t hours. When is the pool empty?
Answer: W(t) = 2000 - 50t; empty at t = 40 hours
Solution: W(t) = 2000 - 50t. Set W(t) = 0: 2000 - 50t = 0, so t = 40 hours.
Question 3: Temperature in Fahrenheit can be found using F(C) = (9/5)C + 32. Find the Fahrenheit temperature when Celsius is 25.
Answer: F(25) = 77 degrees Fahrenheit
Solution: F(25) = (9/5)(25) + 32 = 45 + 32 = 77.
Question 4: A phone plan costs $30/month plus $0.10 per text. If you sent 150 texts, what is your total bill?
Answer: $45
Solution: B(t) = 30 + 0.10t. B(150) = 30 + 0.10(150) = 30 + 15 = 45 dollars.
Question 5: A ball is dropped and bounces to 3/4 of its previous height. If dropped from 64 feet, H(n) = 64(3/4)^n gives height after n bounces. Find H(2).
Answer: H(2) = 36 feet
Solution: H(2) = 64(3/4)² = 64(9/16) = 576/16 = 36 feet.
Question 6: A store sells shirts for $15 each. If S(n) = 15n represents revenue, and they sold 45 shirts, what is the revenue?
Answer: $675
Solution: S(45) = 15(45) = 675 dollars.
Question 7: A car's value depreciates according to V(t) = 25000 - 2500t, where t is years. What is the value after 4 years?
Answer: $15,000
Solution: V(4) = 25000 - 2500(4) = 25000 - 10000 = 15000 dollars.
Question 8: Distance traveled is D(t) = 60t for a car going 60 mph. How long to travel 240 miles?
Answer: 4 hours
Solution: Set D(t) = 240: 60t = 240. Divide by 60: t = 4 hours.
Question 9: A gym membership costs $50 initial fee plus $25 per month. Write C(m) and find the cost for 6 months.
Answer: C(m) = 25m + 50; C(6) = $200
Solution: C(m) = 25m + 50. C(6) = 25(6) + 50 = 150 + 50 = 200 dollars.
Question 10: A rectangle has width w and length 2w + 3. Write the perimeter function P(w) and find P(5).
Answer: P(w) = 6w + 6; P(5) = 36
Solution: P(w) = 2(w) + 2(2w + 3) = 2w + 4w + 6 = 6w + 6. P(5) = 6(5) + 6 = 36.
Next Steps
- Practice writing functions from word descriptions
- Focus on identifying the variable and constant parts
- Move on to common mistakes when ready