Solving Equations

personneedshelp

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May 2, 2009
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Two years ago, Matt planted two trees. Tree X was 24 inches tall when planted, and Tree Y was 40 inches tall when planted. If Tree X grows at a rate of 8 inches per year, and Tree Y grows at a rate of 6 inches per year, after how many more years will Tree X be as tall as Tree Y?

So far, I have the following: Let b = current height of Tree X
24 + 16 = b
b = 40 inches
Let m = current height of Tree Y
40 + 12 = m
m = 52 inches
Let g = height difference between Tree X and Tree Y
52 - 40 = g
g = 12 inches

I know the answer is 6 years with a total height for both trees of 88 inches, but after doing the above, I can't figure out how to write the rest of it. :(
Thank you for your help! :)

When you have to make a choice and don't make it, that in itself is a choice.
~William James
 
tree x height as a function of time:
x=24+8t

tree y's height as a function of time
y=40 + 6t

when will the trees be the same height? when will x=y?
24+8t=40+6t
subtract 6t from each side of = sign
24+8t=40
subtract 24 from each side of = sign
8t= 16
divide both sides by 8
t=2 years answer

Arthur
 
Answer is 8 years.

24 + 8x = 40 + 6x
2x = 16
x = 8

24 + 8*8 = 88
40 + 8*6 = 88
 
arthur ohlsten said:
tree x height as a function of time:
x=24+8t

tree y's height as a function of time
y=40 + 6t

when will the trees be the same height? when will x=y?
24+8t=40+6t
subtract 6t from each side of = sign
24+2t=40 <====Slight typo!
subtract 24 from each side of = sign
2t= 16
divide both sides by 2
t=8 years answer

Arthur
.. :wink:
 
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