SOLUTION: A gardener is planting two types of trees: type A is three feet tall and grows at a rate of 15 inches per year. Type B is four feet tall and grows at a rate of 10 inches per year

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: A gardener is planting two types of trees: type A is three feet tall and grows at a rate of 15 inches per year. Type B is four feet tall and grows at a rate of 10 inches per year      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1031367: A gardener is planting two types of trees: type A is three feet tall and grows at a rate of 15 inches per year. Type B is four feet tall and grows at a rate of 10 inches per year
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In terms of feet:
(A) +y+=+3+%2B+%2815%2F12%29%2Ax+
(B) +y+=+4+%2B+%2810%2F12%29%2Ax+
------------------------
(A) +y+=+%28+5%2F4%29%2Ax+%2B+3+
(B) +y+=+%28+5%2F6+%29%2Ax+%2B+4+
---------------------
Here are the plots of the
2 lines:

------------
To find the intersection, set A = B
++%28+5%2F4%29%2Ax+%2B+3+=+%28+5%2F6+%29%2Ax+%2B+4+
Multiply both sides by +12+
+15x+%2B+36+=+10x+%2B+48+
+5x+=+12+
+x+=+12%2F5+
and
(A) +y+=+%28+5%2F4%29%2A%2812%2F5%29+%2B+3+
(A) +y+=+3+%2B+3+
(A) +y+=+6+
The trees are the same height, 6 ft
in 12/5 years, or 2 yrs 5 months