Colbert's backyard has two trees, shown below. The height of shorter tree is 3/5 of the height of the taller tree. If the height of the shorter tree is 4 1/2 feet tall, what is the height, in feet, of the taller tree? ​

Respuesta :

Answer:

The height of the taller tree is 7.5 feet.

Step-by-step explanation:

I am going to say that:

The height of the shorter tree is x.

The height of the taller tree is y.

The height of shorter tree is 3/5 of the height of the taller tree.

This means that [tex]x = \frac{3y}{5}[/tex]

If the height of the shorter tree is 4 1/2 feet tall, what is the height, in feet, of the taller tree? ​

This means that [tex]x = 4 + \frac{1}{2} = \frac{8+1}{2} = \frac{9}{2}[/tex]

We want to find y.

[tex]x = \frac{3y}{5}[/tex]

[tex]\frac{9}{2} = \frac{3y}{5}[/tex]

[tex]6y = 45[/tex]

[tex]y = \frac{45}{6}[/tex]

[tex]y = 7.5[/tex]

The height of the taller tree is 7.5 feet.