Write a system you would use to solve. Billy's restaurant ordered 200 flowers for Mother's Day. They ordered carnations at $1.50 each, roses at $5.75 each and daisies at $2.60 each. They ordered mostly carnations, and 20 fewer roses than daisies. The total order came to $589.50. How many of each type of flower was ordered?

Number of carnations = 80

Number of roses = 50

Number of daisies = 70

Explanation:

Let,

Number of carnations = c

Number of roses = r

Number of daisies = d

Now,

According to question

1.50c + 5.75r + 2.60d = 589.50 ... (1)

c + r + d = 200 ... (2)

r = d - 20 ... (3)

From (1) and (3), we get

1.50c + 5.75 (d - 20) + 2.60d = 589.50

or

1.50c + 5.75d - 115 + 2.60d = 589.50

or

1.50c + 8.35d = 704.50 ... (4)

From (2) and (3), we get

c + (d - 20) + d = 200

or

c + 2d - 20 = 200

or

c + 2d = 220

or

c = 220 - 2d ... (5)

From (4) and (5), we get

1.50 (220 - 2d) + 8.35d = 704.50

or

330 - 3d + 8.35d = 704.50

or

330 + 5.35d = 704.50

or

5.35d = 374.50

or

d = 70

Substituting value of d in (5)

c = 220 - 2 (70)

or

c = 80

substituting value of d in (3)

r = 70 - 20

or

r = 50

Hence,

Number of carnations = 80

Number of roses = 50

Number of daisies = 70