Chapter 2: Introduction to Linear Polynomials

Exercise

Question

Question: 1

1 / 3

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.

Answer

1
Use the two given observations to find the change in the bill and the change in the number of modules.
Change in bill = 500 - 400 = ₹100
Change in modules count = 14 - 10 = 4
2
Find the cost per module using the changes in the bill and the number of modules.
\text{Cost per module $(a) = \dfrac{100}{4} = ₹25$}
3
Use either observation to identify the values of x and y.
Observation: $x$ = 10 modules, $y$ = ₹400
4
Substitute the values of x, y, and a into the relation to find b.
$y = ax + b$
⇒
\text{ ${color:#2E2EFF}400{/color} = {color:#2E2EFF}25{/color} × {color:#2E2EFF}10{/color} + b$ $\quad$ ${color:#625b5f}[x = 10 modules, y = ₹400, a = ₹25]{/color}$}
⇒
$400 = 250 + b$
⇒
$b = 400 - 250$
⇒
$b = 150$
5
Write the values of a and b.
Answer: $a$ = ₹25 per module, $b$ = ₹150
Sponsored320 x 50