Question 110562: A florist is creating 10 centerpieces for a wedding. The florist can use roses that cost $2.50 each, lilies that cost $4 each, and irises that cost $2 each to make the bouquets. The customer has a budget of $300 and wants each bouquet to contain 12 flowers, with twice as many roses used as the other two types of flowers combined. How many of each type of flower should be in each centerpeice?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A florist is creating 10 centerpieces for a wedding. The florist can use roses that cost $2.50 each, lilies that cost $4 each, and irises that cost $2 each to make the bouquets. The customer has a budget of $300 and wants each bouquet to contain 12 flowers, with twice as many roses used as the other two types of flowers combined. How many of each type of flower should be in each center-peice?
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Let x, y, z = number of roses, lilies, and irises, respectively
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Find the cost per center-piece: 300/10 = $30 each
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Write an equation for each statement
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"The customer has a budget of $300"
2.5x + 4y + 2z = 300/10; (equation for a single center-piece)
2.5x + 4y + 2z = 30
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"wants each bouquet to contain 12 flowers,"
x + y + z = 12
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"twice as many roses used as the other two types of flowers combined".
x = 2(y+z)
x = 2y + 2z
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Substitute (2y + 2z) for x in the 1st equation:
2.5(2y + 2z) + 4y + 2z = 30
5y + 5z + 4y + 2z = 30
9y + 7z = 30
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Substitute (2y+2z) for x in the 2nd equation:
(2y + 2z) + y + z = 12
3y + 3z = 12
Simplify, divide equation by 3:
y + z = 4
y = (4 - z)
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In equation: 9y + 7z = 25, substitute (4-z) of y, find z
9(4-z) + 7z = 30
36 - 9z + 7z = 30
-2z = 30 - 36
-2z = -6
z = -6/-2
z = +3 irises in each
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Remember that y = 4 - z
y = 4 - 3
y = 1 lily
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Then using the 2nd equation:
x + 1 + 3 = 12
x = 12 - 4
x = 8 roses
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Check solution to see if it agrees with the $300 budget:
2.5(8) + 1(4) + 3(2) =
20 + 4 + 6 = 30 * 10 = $300
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You can check and make sure it satisfies the other two equations
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