Let c represents the number of carnations ordered
Let r represents the number of roses ordered
Let d represents the number of daisies ordered
We are told that the total order came to $500 and that they ordered carnations at $1 each,roses at $2 each,and daises $3 each. This information can be represented by
1c + 2r + 3d = 500
c + 2r + 3d = 500_________________equation(1)
Total ordered is 200 flowers.
This can be represented by the equation
c + r + d = 200 _____________________equation (2)
They ordered 20 fewer roses than daisies.
This can be represented by the equation
r = d - 20 _________________________equation(3)
Substitute d = r - 20 into eqaution(1) and equation(2)
c + 2r + 3d = 500
c + 2(d - 20) + 3d = 500
c + 2d - 40 + 3d = 500
c + 5d - 40 = 500
c + 5d = 500 + 40
c + 5d = 540_________________equation (4)
Also,
c + r + d = 200
c + d - 20 + d = 200
c + 2d -20 = 200
c + 2d = 200 + 20
c + 2d =220 _________________eqaution (5)
Solving the two eqautions simultaneously, we have
c + 5d = 540 _________________equation (4)
c + 2d = 220 _________________equation (5)
Sunbtract eqaution (5) from eqaution (4)
3d = 320
d = 320/3
d = 106.67
Substitute d = 106.67 into equation (4)
c + 5d = 540
c + 5(106.67) = 540
c + 533.35 = 540
c = 540 - 533.35
c = 6.65
r = d - 20
r = 106.67 - 20
r=106.67 - 20
r = 86.67
Hence, d = 106.67, c 6.65 and r = 86.67
Rounding off to the nearest whole number,
There are 107 daisies, 7 carnations and 87 roses