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Felipe works in an amusement park and is helping decorate it with strands of lights. This morning, he used a total of 34 strands of lights to decorate 4 bushes and 2 trees. This afternoon, he strung lights on 4 bushes and 4 trees, using a total of 52 strands. Assuming that all bushes are decorated one way and all trees are decorated another, how many strands did Felipe use on each?

Felipe Works In An Amusement Park And Is Helping Decorate It With Strands Of Lights This Morning He Used A Total Of 34 Strands Of Lights To Decorate 4 Bushes An class=

Answer :

Let x and y be the number of strands used to decorate a bush and a tree, respectively. Therefore, the system of equations is

[tex]\begin{cases}4x+2y=34 \\ 4x+4y=52\end{cases}[/tex]

To solve the system using the elimination method, subtract the first equation from the second one; then,

[tex]\begin{gathered} (4x+4y)-(4x+2y)=52-34 \\ \Rightarrow2y=18 \\ \Rightarrow y=9 \end{gathered}[/tex]

Substitute the last result into the second equation,

[tex]\begin{gathered} y=9 \\ \Rightarrow4x+4y=4x+4\cdot9=4x+36 \\ \Rightarrow4x+36=52 \\ \Rightarrow4x=16 \\ \Rightarrow x=4 \end{gathered}[/tex]

Thus, to decorate every bush, we need 4 strands of lights, and for every tree 9 strands of lights

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