Question

A tree grows 1 3/4 per year.How long will it take the tree to grow from a height of 21 1/4 feet to a height of 37 feet?

Answer 1

For this case, the first thing we must do is define variables.

We have then:

x: number of years

y: height of the tree in feet

We write the mixed numbers as decimals:

$1 \frac{3}{4} = 1.75$

$21 \frac{1}{4} = 21.25$

The expression that models the problem is:

$y = 1.75x + 21.25$

By the time the tree reaches a height of 37 feet, we have:

$1.75x + 21.25 = 37$

From here, we uncover the number of years:

$1.75x = 37 - 21.25\\1.75x = 15.75$

$x = \frac{15.75}{1.75}\\x = 9$

Answer:

It will take the tree to grow from a height of 21 1/4 feet to a height of 37 feet about:

$x = 9 years$

Answer 2

A tree grows 1 3/4 = 7/4 feet per year.

If you would like to know how long will it take the tree to grow from a height of 21 1/4 = 85/4 feet to a height of 37 feet, you can calculate this using the following steps:

37 - 21 1/4 = 37 - 85/4 = 148/4 - 85/4 = 63/4 = 15 3/4

15 3/4 / 1 3/4 = 63/4 / 7/4 = 63/4 * 4/7 = 9 years

Result: It will take 9 years.