Let the number of red, blue and green chairs be x, y and z respectively.

total number of chairs = 100

x+y+z=100---->(1)

The cost of a red chair is Rs.240

The cost of a blue chair is Rs.260

the cost of a green chair is Rs.300

The total cost of chair is Rs.25,000

240x+260y+300z=25000---->(2)

divide (2) by 10

24x+26y+30z=2500

divide again by 2

12x+13y+15z=1250 --->(3)

from equation (1)

x+y =100-z

from equation (3)

12x+13y = 1250-15z

take z=k where k is an arbitrary constant and is a real number

so the above equations become

x+y=100-k

12x+13y=1250-15k

| 1 1 |

| 12 13 | = 13-12 = 1 which is not equal to zero.

by cramers rule the equations have a unique solution.

replace the first column in the determinant by 100-k and 1250-15k

1300-13k -1250+15k = 2k+50/1= 2k+50 = x

replace the second column in the determinant by 100-k and 1250-15k

1250-15k -(12)(100-k) = 1250-15k -1200+12k = 50 -3k = y

z = k

k should lie between 0 and 16 since 50-3k should not acquire a negative value.

the solution is ( 2k+50, 50-3k, k ) k lies between 0 and 16

substitute k as 0 you get ( 50,50,0)

when k is 1 you get ( 52,47,1)

when k is 2 you get ( 54,44,2)

the above mentioned solutions are takin in the order of (x,y,z) respectively .