dferm wrote:When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?
A. 3/10
B. 2/5
C. 1/2
D. 2/3
E. 6/5
We also could use the answer choices, which represent the increase in feet each year. Let h= height of tree.
Answer choice C:
After 4 years, h = 4 + 4(1/2) = 6.
After 6 years, h = 6 + 2(1/2) = 7.
7-6=1, but 1/5 * 6 = 6/5. Doesn't work.
1< 6/5, so we need the increase to be greater.
Answer choice D:
After 4 years, h = 4 + 4(2/3) = 20/3.
After 6 years, h = 20/3 + 2(2/3) = 24/3.
24/3 - 20/3 = 4/3, and 1/5 * 20/3 = 4/3. Success!
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