Mathematics
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.
Polynomials
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Answer
Given:
Number of modules accessed (x) and monthly bill (y) follow the relation y = ax + b.
When x = 10, y = 400.
When x = 14, y = 500.
Substituting these values into y = ax + b, we get the following two equations:
400 = 10a + b …(i)
500 = 14a + b …(ii)
From equation (i): b = 400 - 10a
Substituting this into equation (ii):
500 = 14a + (400 - 10a)
⇒ 500 = 14a + 400 - 10a
⇒ 500 = 4a + 400
⇒ 4a = 500 - 400
⇒ 4a = 100
⇒ a =
⇒ a = 25
Substituting a = 25 in b = 400 - 10a:
b = 400 - 10(25)
= 400 - 250
= 150
Hence, a = 25 and b = 150.
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