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31 May, 19:10

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?

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  1. 31 May, 21:09
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    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
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