Ex 2.5, 2

Transcript

Ex 2.5, 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. Given our linear relationship y = ax + b Here, y = Monthly bill (in ₹) x = Number of hours badminton court was used (in GB) We need to find values of a & b Given that when she used the badminton court for 10 hours, her bill was ₹800 Putting y = 800, x = 10 in our equation 800 = a × 10 + b 800 = 10a + b 10a + b = 800 Also, when she used it for 15 hours, her bill was ₹1100 Putting y = 1100, x = 15 in our equation 1100 = a × 15 + b 1100 = 15a + b 15a + b = 1100 Now, our equations are 10a + b = 800 …(1) 15a + b = 1100 …(2) Doing (2) – (1) (15a + b) – (10a + b) = 1100 – 800 15a + b – 10a – b = 300 (15a – 10a) + (b – b) = 300 5a = 300 a = 300/5 a = 60 Putting a = 60 in (1) 10a + b = 800 10 × 60 + b = 800 600 + b = 800 b = 800 – 600 b = 200 Now, putting values of a & b in our expression y = ax + b y = 60x + 200