Example 11 - Chapter 2 Class 9 - Introduction to Linear Polynomials (Ganita Manjari

Transcript

Example 11 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. Given our linear relationship y = ax + b Here, y = Monthly bill (in ₹) x = Amount of data used (in GB) We need to find values of a & b Given that when she used 10 GB, her bill was ₹350 Putting y = 350, x = 10 in our equation 350 = a × 10 + b 350 = 10a + b 10a + b = 350 Also, when she used 20 GB, her bill was ₹550 Putting y = 550, x = 20 in our equation 550 = a × 20 + b 550 = 20a + b 20a + b = 550 Now, our equations are 10a + b = 350 …(1) 20a + b = 550 …(2) Doing (2) – (1) (20a + b) – (10a + b) = 550 – 350 20a + b – 10a – b = 200 (20a – 10a) + (b – b) = 200 10a = 200 a = 200/10 a = 20 Putting a = 20 in (1) 10a + b = 350 10 × 20 + b = 350 200 + b = 350 b = 350 – 200 b = 150 Now, putting values of a & b in our expression y = ax + b y = 20x + 150 Thus, y = 20x + 150 represents the linear relationship between y, the bill amount in Rupees, and x, the number of GB of the internet data used.