SOLUTION: A nursary has a 2ft. plant that will grow 3ft. every year, and a 4ft. plant will grow 1ft. every year, how long will it for the plants to be the same height? How tall will they be?

Question 149483: A nursary has a 2ft. plant that will grow 3ft. every year, and a 4ft. plant will grow 1ft. every year, how long will it for the plants to be the same height? How tall will they be?
Answer by tryin2bhelpful(6) (Show Source): You can put this solution on YOUR website!
Ok, the best way I think to solve this problem is to look at each plant as a line on a graph and at some point they're going to cross. That's when they'll be the same height.
Let's make "x" the number of years and we'll make an equation.
y is going to be the total number of feet the plant is after "x" number of years.
Plant 1: y= 2ft(starting out) + 3ft/year times x number of years so....
y= 2+3x ... you with me?
this can be written as y=3x+2 a common equation for a line.
Plant 2 is going to be the same way....
We start our with 4ft and add 1 ft each year... written as...
y= 1x + 4
or
y=x+4
if you want you can do it algebraically with a system of equations like this...
y= 3x+2
y= x+4
Multiply one equation by a number that will make the Xs opposite...
in this case it's -3
y= 3x+2
(y= x+4) times -3
Then add the two equations together
so...

y= 3x+2
+ -3y= -3x-12
______________
-2y= -10
divide both sides by (-2) and wualla!!
y= 5
When you plug y back into the original equation... you get...
y= 3x+2
(5)= 3x+2
minus 2 on both sides
3=3x
divide by 3 on both sides
x=1 year!!!!
Or, if you would like you can just graph it and see where they intersect!!!

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