An alternative approach that you could have used in this case is working backwards from the answer choices. Since all of the answer choices are fractions, this approach isn't quite as smooth on this problem as it might be on others, but it's still helpful if you get stuck on the algebra.
When working backwards, it's often a good idea to start with C, and then choose to go bigger or smaller from there.
C. 1/2
If the tree increased by 1/2 each year, we can create a chart for the values each year:
year 1: 4.5 ft
year 2: 5 ft
year 3: 5.5 ft
year 4: 6 ft
year 5: 6.5 ft
year 6: 7 ft
Is 7 1/5 taller than 6? No, it's 1/6 taller. Clearly we need to increase by more each year. Try D:
D. 2/3
Again, create a chart:
year 1: 4 and 2/3 ft
year 2: 5 and 1/3
year 3: 6
year 4: 6 and 2/3
year 5: 7 and 1/3
year 6: 8
Is 8 1/5 greater than 6 and 2/3? First, turn 6 and 2/3 into an improper fraction, then multiply by 6/5 (an increase of 1/5):
(20/3)(6/5) = 24/3 = 8
Correct! The answer is D.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
