-162) Castel and Sumalee each improved their yards by planting rose bushes and ornamental grass.They bought their supplies from the same store. Castel spent $69 on 5 rose bushes and 8 bunchesof ornamental grass. Sumalee spent $42 on 2 rose bushes and 8 bunches of ornamental grass.What is the cost of one rose bush and the cost of one bunch of ornamental grass?#2

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Answer :

AavinK9965 AavinK9965 · Answer 1 · 2023-12-20T22:41:36-05:00

Let 'x' and 'y' be the cost of one rose bush and one bunch of ornamental grass.

Given that Castel paid $69 for 5 rose bushes and 8 bunches of grass,

[tex]5x+8y=69\ldots(1)[/tex]

Also, given that Sumalee paid $42 for 2 rose bushed and 8 bunches of grass,

[tex]2x+8y=42\ldots(2)[/tex]

Now that we have two equations and two variables. These can be solved using the Elimination Method.

Subtract equation (2) from (1) as follows,

[tex]\begin{gathered} (5x+8y)-(2x+8y)=69-42 \\ 5x+8y-2x-8y=27 \\ 3x+0=27 \\ x=\frac{27}{3} \\ x=9 \end{gathered}[/tex]

Substitute this value in (1) and obtain the corresponding y-value,

[tex]\begin{gathered} 5(9)+8y=69 \\ 45+8y=69 \\ 8y=69-45 \\ y=\frac{69-45}{8} \\ y=3 \end{gathered}[/tex]

So the simultaneous solution is obtained as,

[tex]\begin{gathered} x=9 \\ y=3 \end{gathered}[/tex]

Thus, the cost of one rose bush is $9 and the cost of one bunch of ornamental grass is $3.