Chapter 2: Introduction to Linear Polynomials

Exercise

Question

Question: 2

2 / 3

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.

Answer

1
Use the two given observations to find the change in the bill and the change in the number of hours.
Change in bill = 1100 - 800 = ₹300
Change in hours = 15 - 10 = 5
2
Find the charge per hour using the changes in the bill and the number of hours.
\text{Charge per hour $(a) = \dfrac{300}{5} = ₹60$ per hour}
3
Use either observation to identify the values of x and y.
Observation: $x$ = 10 hours, $y$ = ₹800
4
Substitute the values of x, y, and a into the relation to find b.
$y = ax + b$
⇒
\text{ ${color:#2E2EFF}800{/color} = {color:#2E2EFF}60{/color} × {color:#2E2EFF}10{/color} + b$ $\quad$ ${color:#625b5f}[x = 10 hours, y = ₹800, a = ₹60]{/color}$}
⇒
$800 = 600 + b$
⇒
$b = 800 - 600$
⇒
$b = 200$
5
Write the values of a and b.
Answer: $a$ = ₹60 per hour, $b$ = ₹200
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