Question

A gardener is planting two types of trees: Type A is 10 feet tall and grows at a rate of 19 inches per year. Type B is 4 feet tall and grows at a rate of 25 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

Answer 1

Answer:

It'll take 12 years

Step-by-step explanation:

Given

Type A:

$Initial\ Height = 10ft$

$Growth = 19in$

Type B:

$Initial\ Height = 4ft$

$Growth = 25in$

Required

Determine the years they'll reach the same height

First, convert feet to inches in both measurements (this is done by multiplying measurement by 12):

Type A:

$Initial\ Height = 10ft$

$Initial\ Height = 10 * 12in$

$Initial\ Height = 120in$

Type B:

$Initial\ Height = 4ft$

$Initial\ Height = 4 * 12in$

$Initial\ Height = 48in$

The height at any year from both trees is calculated using

$Height = Iniital\ Height + Growth * x$

Where x represents the year;

For Type A:

$Height = 120+ 19 * x$

$Height = 120+ 19x$

For Type B:

$Height = 48+ 25 * x$

$Height = 48+ 25x$

To get when their height will be equal, we simply equate both expressions:

$48+ 25x = 120 + 19x$

Collect Like Terms

$25x - 19x= 120 - 48$

$6x= 72$

Solve for x

$x = 72/6$

$x = 12$

Hence, It'll take 12 years