Exercise 2.5 focuses on applying linear equations in real-life situations. In this exercise, students learn how to form equations using given data and determine unknown constants. These problems strengthen algebraic thinking and problem-solving skills.
Exercise 2.5 Solutions
Question 1
A learning platform charges a fixed monthly fee and an additional cost per digital learning module accessed. A student observes that when she accessed 10 modules, her bill was ₹400. When she accessed 14 modules, her bill was ₹500. If the monthly bill y depends on the number of modules accessed, x, according to the relation y = ax + b, find the values of a and b.
Solution
Given: y=ax+b
From data:
When x=10, y=400
So 400=10a+b….(1)
When x=14, y=500
So 500=14a+b….(2)
Subtract (2) from (1)
500−400=(14a+b)−(10a+b)
100=4a
⇒a=25
Substitute into (1)
400=10(25)+b
400=250+b
⇒b=150
Hence a=25,b=150
Question 2
A gym charges a fixed monthly fee and an additional cost per hour for using the badminton court. A student using the gym observed that when she used the badminton court for 10 hours, her bill was ₹800. When she used it for 15 hours, her bill was ₹1100. If the monthly bill y depends on the hours of the use of the badminton court, x, according to the relation y = ax + b, find the values of a and b.
Solution
Given: y=ax+b
From data:
800=10a+b…(1)
1100=15a+b…(2)
Subtract (1) from (2)
300=5a⇒a=60
Substitute into (1):
800=600+b
⇒b=200
Hence a=60,b=200
Question 3
Consider the relationship between temperature measured in degrees Celsius (°C) and degrees Fahrenheit (°F), which is given by °C = a°F + b. Find a and b, given that ice melts at 0 degrees Celsius and 32 degrees Fahrenheit, and water boils at 100 degrees Celsius and 212 degrees Fahrenheit.
Solution
Given relation: °C=a(°F)+b
From data:
When °F=32, then °C=0
So 0=32a+b…(1)
When °F=212, °C=100
So 100=212a+b…(2)
Subtract (1) from (2)
100=180a
So a=95
Substitute into (1)
0=32(95)+b
b=−9160
Hence a=95,b=−9160
Conclusion
This exercise helps students:
- Convert real-life situations into linear equations
- Solve equations using substitution and elimination
- Understand practical applications like billing and temperature conversion
It is an important step toward mastering algebra and analytical thinking.