Question

You are making 5 Autumn Classic bouquets for your friends. You have $610 to spend and want 24 flowers for each bouquet. Roses cost $6 each, tulips cost $4 each, and lilies cost $3 each. You want to have twice as many roses as the other 2 flowers combined in each bouquet. How many roses, tulips, and lilies do you include in each Autumn Classic bouquet?

Answer 1

There are 16 Roses , 2 Tulips , 6 Lilies in each Autumn Classic Bouquet.

Further explanation

Simultaneous Linear Equations could be solved by using several methods such as :

• Elimination Method
• Substitution Method
• Graph Method

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.

$R + T + L = 24$ → 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.

$6R + 4T + 3L = 610 \div 5$

$6R + 4T + 3L = 122$ → Equation 2

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You want to have twice as many roses as the other 2 flowers combined in each bouquet.

$R = 2 ( T + L )$ → Equation 3

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Equation 1  ↔ Equation 3:

$R + T + L = 24$

$2 ( T + L ) + T + L = 24$

$3T + 3L = 24$

$T + L = 8$

$T = 8 - L$→ Equation 4

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Equation 4  ↔ Equation 3:

$R = 2 ( T + L )$

$R = 2 ( 8 - L + L )$

$R = 2 ( 8 )$

$\boxed{R = 16}$

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Equation 2  ↔ Equation 4:

$6R + 4T + 3L = 122$

$6(16) + 4(8 - L) + 3L = 122$

$96 + 32 - 4L + 3L = 122$

$L = 96 + 32 - 122$

$\boxed{L = 6}$

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Equation 4:

$T = 8 - L$

$T = 8 - 6$

$\boxed{T = 2}$

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Conclusion:

There are 16 Roses , 2 Tulips , 6 Lilies in each Autumn Classic Bouquet.

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Learn more

• Perimeter of Rectangle : brainly.com/question/12826246
• Elimination Method : brainly.com/question/11233927
• Sum of The Ages : brainly.com/question/11240586

Answer details

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations