### Brain Teasers

# How Old is the House?

Gretchen and Henry were looking to buy a house together, and finally found one with a beautifully landscaped yard, plenty of bedrooms, and a beautiful tree out front. They asked the owner how old the house was, and this was his reply:

"I planted that tree when the house was built. It was 7 feet tall at the time. It has grown 3 feet each year, and at the end of this past full year, it was four times its original height."

"But how old is the house?" asked Henry.

Gretchen said, "Don't be so dense. He just told us."

So, how old is the house?

"I planted that tree when the house was built. It was 7 feet tall at the time. It has grown 3 feet each year, and at the end of this past full year, it was four times its original height."

"But how old is the house?" asked Henry.

Gretchen said, "Don't be so dense. He just told us."

So, how old is the house?

### Answer

The house is 7 years old.The tree height is 28 feet, since it is four times its original height.

To figure out the age of the tree, let x = age of the tree in years. The height of the tree is then 7 + 3x. Since we know that the tree is now 28 feet, we can say:

28 = 7 + 3x

21 = 3x

7 = x

So the tree must be 7 years old, making the house just as old.

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