Case Study Questions on Comparing Quantities
In a Maths class, students often encounter real-life scenarios where they need to compare quantities. Here are some effective case study questions along with detailed explanations.
Case Study 1: Comparing Prices of Fruits
*Scenario*: A fruit vendor sells apples and oranges. The vendor sells apples at $3 per kg and oranges at $2 per kg.
*Question*: If a customer buys 5 kg of apples and 7 kg of oranges, what is the total cost? Compare the total cost of both fruits.
*Answer*:
- Cost of apples = 5 kg * $3/kg = $15
- Cost of oranges = 7 kg * $2/kg = $14
- Total cost = Cost of apples + Cost of oranges = $15 + $14 = $29
The total cost of apples is greater than that of oranges by $1.
Case Study 2: Discounts on Electronics
*Scenario*: A student wants to buy a laptop priced at $800 with a 15% discount and a tablet priced at $300 with a 10% discount.
*Question*: What is the final price of each item after applying the discount? Which item offers a better discount in terms of money saved?
*Answer*:
- Discount on laptop = 15% of $800 = $120
- Final price of laptop = $800 - $120 = $680
- Discount on tablet = 10% of $300 = $30
- Final price of tablet = $300 - $30 = $270
The laptop saves $120, while the tablet saves $30. The laptop offers a better discount.
Case Study 3: Distance and Speed Comparison
*Scenario*: Two cyclists, A and B, travel different distances at different speeds. Cyclist A travels 60 km at a speed of 20 km/h, while Cyclist B travels 80 km at a speed of 25 km/h.
*Question*: Who reaches their destination first? Compare their travel times.
*Answer*:
- Time taken by Cyclist A = Distance/Speed = 60 km / 20 km/h = 3 hours
- Time taken by Cyclist B = 80 km / 25 km/h = 3.2 hours
Cyclist A reaches the destination first, arriving 0.2 hours (12 minutes) earlier than Cyclist B.
These case studies help students understand practical applications of comparing quantities.