priyasom Posted January 21, 2008 Share Posted January 21, 2008 I found this problem in PowerPrep. 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 end of the 4th year. By how many feet did the tree increase each year? a) 3/10 b) 2/5 c) 1/2 d) 2/3 e) 6/5 Ans: d Can someone explain this one to me? I couldn't get the OA. Quote Link to comment Share on other sites More sharing options...
vgp Posted January 21, 2008 Share Posted January 21, 2008 I can’t attach any drawings, sorry. Ok lets say X-is the length of the tree by the end of the 4-th year then by the end of the 6-th year it would be x+x/5 = 6x/5 Now we need to find for the fifth year in order to find out the growth rate. As long as the growth rate is constant it would be the arithmetic mean of 6-th and 4-th years (6x/5+x)/2= 11x/10. Now we can find out the growth rate per year. 11x/10-x or 6x5-11x/10, which ever you want J it equals to X/10 Now we know everything we need, x-3x/10= 7x/10 (this is the lenght by the end of the first year!). At the beginning of the first year the length was 4 So, 4+x/10=7x/10 x= 40/6 --- but this is the length of the tree by the end of the fourth year!!! Tree grows (remember X/10?! Look up)by 40/6/10 = 2/3 Quote Link to comment Share on other sites More sharing options...
vgp Posted January 21, 2008 Share Posted January 21, 2008 I'm so proud I've earned 1 strawberry :) Quote Link to comment Share on other sites More sharing options...
yowas Posted January 22, 2008 Share Posted January 22, 2008 Another way to look at it: Make a chart of the growth: x = Constant amount tree grows each year Planted: 4 feet After 1 Year: 4 + x feet After 2 Years: 4 + 2x feet .... After 4 Years: 4 + 4x feet ... After 6 years: 4 + 6x feet From the question it says "At the end of the 6th year, the tree was 1/5 taller than it was at end of the 4th year. " From this combined with the table, setup the equation. 4 + 6x = (1 + 1/5)*(4 + 4x) 1.2x = .8 x = .667 or 2/3 Quote Link to comment Share on other sites More sharing options...
AKSTCS Posted January 22, 2008 Share Posted January 22, 2008 My take:- 4+6x =(1+ 1/5)*(4+4x) =>4+6x =(6/5)*4+4x =>20+30x = 24 + 24x =>6x=4 =>x=4/6=2/3 Thus D. Quote Link to comment Share on other sites More sharing options...
sangeethai Posted January 22, 2008 Share Posted January 22, 2008 can someone explain why 1+1/5?? Quote Link to comment Share on other sites More sharing options...
pasu Posted January 22, 2008 Share Posted January 22, 2008 can someone explain why 1+1/5?? since the height is 1/5th of what it was in the 4th year, you need to find out what is 1/5th of the 4th years height and then add that to the 4th year height. Look at it this way. 4+6x= 1/5(4+4x) + (4+4x). Hope this makes sense. Quote Link to comment Share on other sites More sharing options...
priyasom Posted January 23, 2008 Author Share Posted January 23, 2008 Thanks to all of you. Quote Link to comment Share on other sites More sharing options...
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