A gym charges a fixed monthly fee and an additional cost per hour for using the badminton court. Class 9

A gym charges a fixed monthly fee and an additional cost per hour for using the badminton court. Class 9

Question 1.

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. Class 9

Solution:

Number of hours the badminton court was used = x

Total monthly bill = y

According to the given conditions,

When x = 10, y = 800, and

When x = 15, y = 1100

Substituting the values of x and y in y = ax + b,we get

800 = 10a + b ...(i)

1100 = 15a + b ...(ii)

From (i),

b = 800 - 10a ...(iii)

Substituting b = 800 - 10a in equation (ii), we get

1100 = 15a+ (800-10a)

∴ 1100 = 5a+ 800

∴ 5a = 1100 - 800

∴ 5a = 300

∴ a = $\frac{300}{5}$ = 60

Substituting a = 60 in (iii), we get

b = 800 - 10(60) = 800 - 600

∴ b = 200

∴ The value of a is ₹ 60, and the value of b is ₹ 200.