Question

The height of a tree house is five times the height of a dog house. If the tree house is 16 feet taller than the dog house, how tall is the tree house?

Answer 1

The treehouse is 20 feet tall

Explanation:

Let's call the height of the treehouse T, and the height of the doghouse D

So, we know two things:

First, the height of the treehouse is 5 times the height of the dog house. This can be represented as:

T=5(D)

Second, the treehouse is 16 feet taller than the doghouse. This can be represented as:

T=D+16

Now, we have two different equations that each have T in them. So instead of saying T=D+16, we can say:

5(D) = D + 16
[because we know that T = 5(D)]

Now, we can solve the equation by subtracting D from both sides

5(D) = D + 16

4(D) = 16

Therefore, D = 16`-:`4

And D = 4

The height of the doghouse is 4 feet. Now, we can take this number and substitute it back into either of the first two equations:

T = 5(4)

or

T = 4 + 16

In either case, T = 20. The treehouse is 20 feet tall