Question

A lending library has fixed charges for the first 3 days and an additional charge for each day there after Raju paid Rs 24 for a book kept for five days .Write a linear equation for this and find 4 solutions for this equation.

Answer 1

Let the fixed charge for first 3 days = ₹x
Per day charge thereafter be ₹y

Total amount paid by Raju after 5 days = ₹ 24

According to the question,

Total amount paid by Raju after 5 days = ₹ 24
Fixed charge + per day charge after 3 days= ₹24

x + (5-3)y= 24

x + 2y = 24 ………..(1)

Hence, the linear equation be x + 2y = 24

Put x = 2 in eq 1

x + 2y = 24

2+ 2y= 24

2y= 24-2

2y = 22

y= 22/2= 11

y= 11

Put x = 4 in eq 1

x + 2y = 24

4+ 2y= 24

2y= 24-4

2y = 20

y= 20/2= 10

y= 10

Put x = 6 in eq 1

x + 2y = 24

6+ 2y= 24

2y= 24-6

2y = 18

y= 18/2= 9

y= 9

Put x = 8 in eq 1

x + 2y = 24

8+ 2y= 24

2y= 24-8

2y = 16

y= 16/2= 8

y= 8

Ist Solution : x= 2, y= 11
2nd Solution: x= 4, y= 10
3rd Solution: x= 6, y= 9
4th Solution: x= 8, y= 8

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