Question

You are planning an ornamental garden that has a total area of 200 square feet. There are two sizes of ornamental plants you have chosen for your garden. Each small plant requires 2.5 square feet of space and each large plant requires 8 square feet of space. This situation can be modeled by the equation 2.5x + 8y = 200 where x is the number of small plants and y is the number of large plants to be placed in the garden. What do the intercepts mean in this situation? What are three possible numbers of small plants and large plants that you can plant in the garden?

Answer 1

\[\huge 2.5\color{salmon}{x}+8\color{plum}{y}=200\]So the second part shouldn't be too difficult. You just plug a number into one of the variables and solve for the other.


Let's say we wanted 10 large plants.\[\huge 2.5\color{salmon}{x}+8(\color{plum}{10})=200\]\[\huge 2.5\color{salmon}{x}+80 =200\]Subtracting 80 from each side gives us,\[\huge 2.5\color{salmon}{x}=120\]Divide both sides by 2.5,\[\huge \color{salmon}{x}=48\]

We've determined that we can fit 10 large, and 48 small plants into the garden.
Try some other numbers, try to get whole numbers. So you don't have a partial plant in the garden.

I would recommend plugging numbers into the Large plant.

Answer 2

What do the intercepts mean?
Hmm, well the intercepts occur when,\[\huge \color{salmon}{x}=0 \qquad \color{royalblue}{\text{or when}} \qquad \color{plum}{y}=0\]

Think of what would happen if you plugged ZERO in for one of the variables, what would that represent?

Answer 3

Thanks so much it makes a lot more sense now.