A gardener is planting two types of trees: Type A is 3 feet tall and grows at the rate of 13 inches per year. Type B is 10 feet tall and grows at a rate of 6 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

Solution:

Let "x" be the number of years

Type A is 3 feet tall and grows at the rate of 13 inches per year

1 feet = 12 inches

3 feet = 3 x 12 = 36 inches

Equation: 36 + 13x eqn 1

Type B is 10 feet tall and grows at a rate of 6 inches per year

10 feet = 120 inches

Equation: 120 + 6x eqn 2

For both trees to be of same height, eqn 1 must be equal to eqn 2

36 + 13x = 120 + 6x

13x - 6x = 120 - 36

7x = 84

x = 12

Thus it takes 12 years for both trees to be of same height

yes, gavin is right.

step-by-step explanation:

gavin is correct. 

this problem is about converting 9% per year to how many percent per quarter. the rate is still the same. it only differed in the time period. so, through dimensional analysis,

9% per year  × (1 year / 4 quarters) = 2.25% per quarter

if he was asked to convert 9% per year to how many percent per quarter  compounded quarterly, then you will not simply divide by four. this is because compounding is not linear.

hope this , have a good day. c;