Question

A gardener is planting two types of trees: Type A is 2 feet tall and grows at a rate of 17 inches per year. Type B is 7 feet tall and grows at a rate of 12 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

Answer 1

Answer: 12 years

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Step-by-step explanation:

x = number of years

y = height in inches

Plant A's equation would be y = 17x+24 since it starts off at 24 inches (2 feet), and grows by 17 inches per year. Note how I'm using inches only. I'm not mixing feet with inches. All units must be the same so we can add properly.

Plant B's equation would be y = 12x+84 for similar reasoning as above. This time the plant starts at 84 inches (equivalent to 7 feet since 7*12 = 84) and grows by 12 inches per year.

Let's solve for x and y

y = 12x+84

17x+24 = 12x+84 .... replace y with 17x+24

17x+24-12x = 12x+84-12x ... subtract 12x from both sides

5x+24 = 84

5x+24-24 = 84-24 ... subtract 24 from both sides

5x = 60

5x/5 = 60/5 ... divide both sides by 5

x = 12

At year 12 is when the two plants will be the same height

Plant A: y = 17x+24 = 17*12+24 = 228 inches

Plant B: y = 12x+84 = 12*12+84 = 228 inches

In 12 years, both plants will be 228 inches tall

note: 228 inches = 19 feet since 228/12 = 19