Question

A Gardner plants two trees
Type A is 9 feet tall and grows a rate of 17 inches per year
Type b is 2 feet tall and grows a rate of 24 in per year
Algebraically determine exactly how many years it will take for these trees to be the same height

Answer 1

Answer:

After 12 yrs the height of both trees type A and type B will be same.

Step-by-step explanation:

Given,

Height of Type A at the time of planting = $9\ ft=9\times12=108\ in$

Height of Type B at the time of planting =  $2\ ft=2\times12=24\ in$

Let the number of years be 'x'.

After 'x' years height of Type A = $108+17x$

After 'x' years height of Type B = $24+24x$

We have to find out the number of years will take for these trees to be the same height.

Now according to question, after 'x' years the height of plant type A and plant type B will be equal.

$108+17x=24+24x$

Combining the like terms, we get;

$24x-17x=108-24\\\\7x=84\\\\x=\frac{84}{7}=12\ yrs$

Hence After 12 yrs the height of both trees type A and type B will be same.