A telecom company charges a fixed monthly fee and an additional cost per GB of the internet data used Class 9

A telecom company charges a fixed monthly fee and an additional cost per GB of the internet data used Class 9

Question 1.

A telecom company charges a fixed monthly fee and an additional cost per GB of the internet data used. A student observes that when she used 10 GB, her bill was ₹350. When she used 20 GB, her bill was ₹550. If the monthly bill y depends on the amount of data used, x (in GB), according to the relation y = ax + b, find the values of a and b. Class 9

Solution:

Number of GB of internet data used = x

Total monthly bill = y

Step I: Using the given condition, obtain two equations

According to the given conditions,

When x = 10, y = 350, and

When x = 20, y = 550

Substituting the values of x and y in the equation y = ax + b, we get

350 = 10a + b ...(i)

550 = 20a + b ...(ii)

Step II: Express b in terms of a using equation (i),

b = 350 - 10a ...(iii)

Step III: Substitute b = 350 - 10a in equation (ii), and solve

550 = 20a + (350 - 10a)

∴ 550 = 10a + 350

∴ 10a = 550 - 350

∴ 10a = 200

∴ a = 20

Step IV: Substitute a = 20 in equation (iii), and solve

b = 350 -10 (20) = 350 -200

∴ b = 150

Step V: Write the equation

Substituting the values of a and b in

y = ax + b, we get

y = 20x + 150

∴ The value of a is 20, and the value of b is 150.