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?
1 Answer
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
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