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27. Eduardo and Dan each improved their yards by planting hostas and shrubs. Theybought their supplies from the same store. Eduardo spent $39.00 on 4 hostas and 3 shrubs.Dan bought 1 hosta and 9 shrubs and spent $84.00. What is the cost of each plant?

Respuesta :

We have hostas (H) and shrubs (S).

Let H be the price of the hostas and S the price of the shrubs.

Then, as Eduardo spent $39 on 4 hostas and 3 shrubs, we can write:

[tex]4H+3S=39[/tex]

For Dan, who bought 1 hosta and 9 shrubs and spent $84, we can write:

[tex]H+9S=84[/tex]

Then, we can clear H from the last equation and replace it in the first one:

[tex]H+9S=84\longrightarrow H=84-9S[/tex][tex]\begin{gathered} 4H+3S=39 \\ 4(84-9S)+3S=39 \\ 4\cdot84-4\cdot9S+3S=39 \\ 336-36S+3S=39 \\ -33S=39-336 \\ -33S=-297 \\ S=\frac{-297}{-33} \\ S=9 \end{gathered}[/tex]

Then, knowing that the price of the shrubs is S=9, we can calculate H:

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