A lending library has a fixed charge for the first three days and an additional charge for each day thereafter.

Solution:

Let the fixed charge for first three days and each day charge thereafter be Rs x and Rs y respectively.
According to the question,
x + 4y = 27 ... (i)
x + 2y = 21 ... (ii)
Subtracting equation (ii) from equation (i), we get
2y = 6
y = 3 ... (iii)
Putting in equation (i), we get
x + 12 =27
x = 15
Hence, fixed charge = Rs 15 and Charge per day = Rs 3.

Total charges paid by Aarushi is given by

27 = x + 4y

x + 4y = 27

This is the required linear equation for the given information.

Aarushi paid Rs 27, of which Rs. x for the first three days and Rs. y per day for 4 more days is given by 

x + (7 – 3) y = 27 

x + 4y = 27 

Above equation represents the linear equation for the given information.

Given, 

Lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Aarushi paid Rs. 27 for a book kept for seven days. If fixed charges are Rs. x and per day charges are Rs. y. 

⇒ 3 × x + (7 – 3) × y = 27 

⇒ 3x + 4y = 27

Let the fixed charge and the charge for each extra day be ‘a’and ‘b’ respectively.

Given, a lending library has a fixed charge for the first three days and an additional charge for each day thereafter Saritha paid Rs 27 for a book kept for seven days

⇒ a + 4b = 27 -------- (1)

Susy paid Rs 21 for the book she kept for five days

⇒ a + 2b = 21 --------- (2)

Subtracting eq2 from eq1

⇒ 2b = 6

⇒ b = 3

Putting this value in eq(1), we get

⇒ a + 4(3) = 2

⇒ a = 27 - 12

⇒ a = 15

Therefore, fixed charge,

a = 15

Rupees and charge thereafter,

b = 3

Rupees per day

⇒ a = Rs. 15