Let's work through another real world example together You are working on a garden plan for the new season and know that you want to plant many new fruits and vegetables you're
having trouble figuring out the best plan because there are so many options. You know that the fruit plants come with two tiny
plants in the one container, and veggies only come with one plant in the container, and you only have spots for 60 plants. The
equation to represent this relationship can be written as 2x + y = 60, when the number of fruit containers you buy, and
y the number of vegetable containers you buy
The other big factor is cost. Fruit containers cost $2 each and vegetable containers cout $1.50 each. You would like to spend
$75. Using the same variables as before the equation to represent total cost of your plants can be written as 2c +1.50 - 75.
A good first step is to rewrite both equations in slope intercept form. We'l start with the equation for price:
2x +1.50y - 75
First, subtract 2 from each side to get
1.50y-2x + 75
Now, we'll divide by 1.5 on both sides and use the cakulator to simply to- overall our new equation isy - -** +50.
What about our equation for total number of plants? If we start with 2-60, what is slope intercept form?
Listed together, our two equations in slope intercept formare
y=- 4/3x+50
Y=-2 + 60
Graph this system of equations on a coordinate plane to solve the system. Remember to check your answer in both equations.
The solution to both equations, and the solution to the system is
This means you should buy
truit containers and
veggie containers to meet your budget and space constraints.