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.
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Question

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.

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KnowledgeBoat · Accepted 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.

Mathematics

Polynomials

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