A gardener is planting two types of trees:
Type A is 6 feet tall and grows at a rate of 10 inches per year.
Type B is 5 feet tall and grows at a rate of 13 inches per year
Algebraically determine exactly how many years it will take for these trees to be the same height.

5 1/2 years

Step-by-step explanation:

Don't forget to convert the current height of the tree into inches, since the current height is in feet and the growth rate is in inches.  

y=number of years

.

Height of Type A=36+15y

Height of Type B=48+10y

.

For height Type A to equal height Type B:

For height Type A to equal height Type B:

Height Type A=Height Type B

36+15y=48+10y . Subtract 36+10y from each side

5y=12

y=5/12

.

ANSWER: It will take 5 months (5/12 years) for the trees to be equal in height.

The irrational number is 12.

Have a day!