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Monique has two artificial christmas trees In her apartme t the taller tree is 12 inches shorter than 5 times the height of the smaller tree of she stacked the shorter tree on top of the taller tree they would be a total of 60 inches tall find the heights of the taller tree and the shorter tree

Respuesta :

lindseyskate1oyiaa4
Hey!~

The two trees are 12 and 48 inches tall.

Hope this helps and have a great day!

-Lindsey

Answer:

The taller tree is 48 inches, and the smaller tree is 12 inches height.

Step-by-step explanation:

Givens

  • The taller tree is 12 inches shorter than 5 times the smaller tree.
  • The sum of both tree's height is 60 inches.

First, we have to expresses each sentence into an equation

[tex]T=5S-12[/tex]

Where [tex]T[/tex] is the taller tree, and [tex]S[/tex] is the smaller tree.

This relation expresses that the taller tree is 12 inches shorter than 5 times the smaller tree.

[tex]T+S=60[/tex]

Because they sum of both height is 60 inches.

Now, we replace the first equation into the second one, and solve for [tex]S[/tex]

[tex]5S-12+S=60\\6S=60+12\\S=\frac{72}{6}=12[/tex]

Then, we replace this value in one equation to find the other variable

[tex]T+S=60\\T+12=60\\T=60-12=48[/tex]

Therefore, the taller tree is 48 inches, and the smaller tree is 12 inches height.

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