Mjkourtis wrote:When a tree was first planted, it was 4 ft. tall. The height increased by a constant each year for the next 6 years. At end, it was 1/5 taller than it was at the end of 4 years. By how many feet did the height increase each year?
A. 3/10
B. 2/5
C. 1/2
D. 2/3
E. 6/5
We can plug in the answers, which represent the growth each year.
Since the height in the 6th year is 6/5 the height in the 4th year, the needed ratio is 6th year : 4th year = 6:5.
Answer choice C: 1/2 each year.
4th year = 4 + 4(1/2) = 6.
6th year = 6 + 2(1/2) = 7.
6th : 4th = 7:6.
Since 7/6 is just a bit less than 6/5, the difference between the 6th year and the 4th year needs to increase by just a little.
The correct answer is
D.
Note that, to determine the correct answer, we had to try only ONE answer choice -- a very efficient way to solve the problem.
Answer choice D: 2/3 each year.
4th year = 4 + 4(2/3) = 20/3.
6th year = 20/3 + 2(2/3) = 24/3.
6th : 4th = 24:20 = 6:5.
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