Question

A gardener is planting two types of trees:

Type A is 9 feet tall and grows at a rate of 6 inches per year.

Type B is 10 feet tall and grows at a rate of 3 inches per year.

Algebraically determine exactly how many years it will take for these trees to be the same height.

Answer 1

Explanation:

let y represent number of years...

9 ft tall = (12 * 9) = 108 inches

10 ft tall = (12 * 10) = 120 inches

Type A : 9 ft (or 108 inches) and grows 6 inches per year..

108 + 6y

Type B : 10 ft (or 120 inches) and grows 3 inches per yr

120 + 3y

how many years will it take them to be the same height...so when will they be equal....so set them equal and solve for y

108 + 6y = 120 + 3y

6y - 3y = 120 - 108

3y = 112

y = 112/3

y = 37 1/3 years....or 37 years and 4 months <====

check...

108 + 6(37 1/3) = 120 + 3(37 1/3)

108 + 6(112/3) = 120 + 3(112/3)

108 + 672/3 = 120 + 336/3

672/3 - 336/3 = 120 - 108

336/3 = 112

112 = 112 (correct)