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.
Polynomials
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Question

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.

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KnowledgeBoat · Accepted Answer

Given:

Number of hours of court use (x) and monthly bill (y) follow the relation y = ax + b.

When x = 10, y = 800.

When x = 15, y = 1100.

Substituting these values into y = ax + b, we get the following two equations:

800 = 10a + b …(i)

1100 = 15a + b …(ii)

From equation (i): b = 800 - 10a

Substituting this into equation (ii):

1100 = 15a + (800 - 10a)

⇒ 1100 = 15a + 800 - 10a

⇒ 1100 = 5a + 800

⇒ 5a = 1100 - 800

⇒ 5a = 300

⇒ a = $\dfrac{300}{5}$

⇒ a = 60

Substituting a = 60 in b = 800 - 10a:

b = 800 - 10(60)

= 800 - 600

= 200

Hence, a = 60 and b = 200.