SOLUTION: You plant a 4 foot maple tree that grows at a rate of 6 inches per year and a 2 foot birch tree that grows a t a rate of 8 inches a year. In how many years will they be the same he

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: You plant a 4 foot maple tree that grows at a rate of 6 inches per year and a 2 foot birch tree that grows a t a rate of 8 inches a year. In how many years will they be the same he      Log On


   

Question 75367: You plant a 4 foot maple tree that grows at a rate of 6 inches per year and a 2 foot birch tree that grows a t a rate of 8 inches a year. In how many years will they be the same height? What is that height?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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You plant a 4 foot maple tree that grows at a rate of 6 inches per year and a 2 foot birch tree that grows a t a rate of 8 inches a year. In how many years will they be the same height? What is that height?
:
Let t = number of years when they are the same height in inches
:
Convert initial heights to inches:
Maple: 12*4 = 48"
Birch: 12*2 = 24"
:
Birch ht = Maple ht
8t + 24 = 6t + 48
8t - 6t = 48 - 24
2t = 24
t = 24/2
t = 12 yrs to be the same height
:
Find the height (also checks our solution:
Maple: 6(12) + 48 = 120" or 10 ft
Birch: 8(12) + 24 = 120" or 10 ft