Question

A gardener is planting two types of trees:

Type A is 7 feet tall and grows at a rate of 11 inches per year.
Type B is 8 feet tall and grows at a rate of 9 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the
same height
Answer:​

Answer 1

6 years

Step-by-step explanation:

The subject Mathematics (not Spanish); however, the solution is as follows...

Given

Height of Type A: 7ft

Growth of Type A = 11in per year

Height of Type B: 8ft

Growth of Type B = 9in per year

Required

When both trees would have the same height

First, the units of height and growth of both trees must be the same.

So, we'll convert the height from feet to inches

Given that 1 foot = 12 inches

Height of Type A: 7 * 12 inches = 84 inches

Height of Type B: 8 * 12 inches = 96 inches

Let y represent the number of years, both trees would have the same height

Type A can be represented algebraically as : 84 + 11y

Type B can be represented algebraically as : 96 + 9y

To solve further, we have to equate both expressions

`Type\ A = Type\ B`

`84 + 11y = 96 + 9y`

Collect Like Terms

`11y - 9y = 96 - 84`

`2y = 12`

Divide both sides by 2

`(2y)/(2) = (12)/(2)`

`y = (12)/(2)`

`y = 6\ years`