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
3 Likes

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.

Polynomials

3 Likes

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 = ⇒ a = 60 Substituting a = 60 in b = 800 - 10a: b = 800 - 10(60) = 800 - 600 = 200 Hence, a = 60 and b = 200.

Mathematics

Polynomials

Related Questions

Identify other points on the line y = 2x + 1 by completing the following table.
x y
1 3
2
5
7 15
9
12
20

Mathematics

Polynomials

Related Questions

Identify other points on the line y = 2x + 1 by completing the following table.xy132571591220

Identify other points on the line y = 2x + 1 by completing the following table.
x y
1 3
2
5
7 15
9
12
20