There are 16 Roses , 2 Tulips , 6 Lilies in each Autumn Classic Bouquet.
<h3>Further explanation</h3>
Simultaneous Linear Equations could be solved by using several methods such as :
- <em>Elimination Method</em>
- <em>Substitution Method</em>
- <em>Graph Method</em>
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!
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<em>Let For Each Bouguet:</em>
<em>Number of Roses = R</em>
<em>Number of Tulips = T</em>
<em>Number of Lilies = L</em>
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<em>There are 24 flowers for each bouquet.</em>
→ <em>Equation 1</em>
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<em>You have $610 to spend for 5 bouguets.</em>
<em>Roses cost $6 each, tulips cost $4 each, and lilies cost $3 each.</em>
![6R + 4T + 3L = 610 \div 5](https://tex.z-dn.net/?f=6R%20%2B%204T%20%2B%203L%20%3D%20610%20%5Cdiv%205)
→ <em>Equation 2</em>
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<em>You want to have twice as many roses as the other 2 flowers combined in each bouquet.</em>
→ <em>Equation 3</em>
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<em>Equation 1 ↔ Equation 3:</em>
![R + T + L = 24](https://tex.z-dn.net/?f=R%20%2B%20T%20%2B%20L%20%3D%2024)
![2 ( T + L ) + T + L = 24](https://tex.z-dn.net/?f=2%20%28%20T%20%2B%20L%20%29%20%2B%20T%20%2B%20L%20%3D%2024)
![3T + 3L = 24](https://tex.z-dn.net/?f=3T%20%2B%203L%20%3D%2024)
![T + L = 8](https://tex.z-dn.net/?f=T%20%2B%20L%20%3D%208)
→ <em>Equation 4</em>
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<em>Equation 4 ↔ Equation 3:</em>
![R = 2 ( 8 - L + L )](https://tex.z-dn.net/?f=R%20%3D%202%20%28%208%20-%20L%20%2B%20L%20%29)
![R = 2 ( 8 )](https://tex.z-dn.net/?f=R%20%3D%202%20%28%208%20%29)
![\boxed{R = 16}](https://tex.z-dn.net/?f=%5Cboxed%7BR%20%3D%2016%7D)
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<em>Equation 2 ↔ Equation 4:</em>
![6R + 4T + 3L = 122](https://tex.z-dn.net/?f=6R%20%2B%204T%20%2B%203L%20%3D%20122)
![6(16) + 4(8 - L) + 3L = 122](https://tex.z-dn.net/?f=6%2816%29%20%2B%204%288%20-%20L%29%20%2B%203L%20%3D%20122)
![96 + 32 - 4L + 3L = 122](https://tex.z-dn.net/?f=96%20%2B%2032%20-%204L%20%2B%203L%20%3D%20122)
![L = 96 + 32 - 122](https://tex.z-dn.net/?f=L%20%3D%2096%20%2B%2032%20-%20122)
![\boxed{L = 6}](https://tex.z-dn.net/?f=%5Cboxed%7BL%20%3D%206%7D)
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<em>Equation 4:</em>
![T = 8 - L](https://tex.z-dn.net/?f=T%20%3D%208%20-%20L)
![T = 8 - 6](https://tex.z-dn.net/?f=T%20%3D%208%20-%206)
![\boxed{T = 2}](https://tex.z-dn.net/?f=%5Cboxed%7BT%20%3D%202%7D)
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<h2>Conclusion:</h2>
There are 16 Roses , 2 Tulips , 6 Lilies in each Autumn Classic Bouquet.
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<h3>Learn more</h3>
<h3>Answer details</h3>
Grade: High School
Subject: Mathematics
Chapter: Simultaneous Linear Equations
Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations