There are 16 Roses , 2 Tulips , 6 Lilies in each Autumn Classic Bouquet.
Simultaneous Linear Equations could be solved by using several methods such as :
If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.
Let us tackle the problem!
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Let For Each Bouguet:
Number of Roses = R
Number of Tulips = T
Number of Lilies = L
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There are 24 flowers for each bouquet.
[tex]R + T + L = 24[/tex] → Equation 1
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You have $610 to spend for 5 bouguets.
Roses cost $6 each, tulips cost $4 each, and lilies cost $3 each.
[tex]6R + 4T + 3L = 610 \div 5[/tex]
[tex]6R + 4T + 3L = 122[/tex] → Equation 2
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You want to have twice as many roses as the other 2 flowers combined in each bouquet.
[tex]R = 2 ( T + L )[/tex] → Equation 3
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Equation 1 ↔ Equation 3:
[tex]R + T + L = 24[/tex]
[tex]2 ( T + L ) + T + L = 24[/tex]
[tex]3T + 3L = 24[/tex]
[tex]T + L = 8[/tex]
[tex]T = 8 - L[/tex]→ Equation 4
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Equation 4 ↔ Equation 3:
[tex]R = 2 ( T + L )[/tex]
[tex]R = 2 ( 8 - L + L )[/tex]
[tex]R = 2 ( 8 )[/tex]
[tex]\boxed{R = 16}[/tex]
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Equation 2 ↔ Equation 4:
[tex]6R + 4T + 3L = 122[/tex]
[tex]6(16) + 4(8 - L) + 3L = 122[/tex]
[tex]96 + 32 - 4L + 3L = 122[/tex]
[tex]L = 96 + 32 - 122[/tex]
[tex]\boxed{L = 6}[/tex]
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Equation 4:
[tex]T = 8 - L[/tex]
[tex]T = 8 - 6[/tex]
[tex]\boxed{T = 2}[/tex]
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There are 16 Roses , 2 Tulips , 6 Lilies in each Autumn Classic Bouquet.
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Grade: High School
Subject: Mathematics
Chapter: Simultaneous Linear Equations
Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations
