To model the situation provided, let's break down the information given:

1. Vinca plants cost $1.20 each.
2. Phlox plants cost $2.50 each.
3. The gardener has enough funds to buy 125 vinca plants and 60 phlox plants in some combination.

Let's denote:

• $x$ as the number of vinca plants.
• $y$ as the number of phlox plants.

Since the gardener can spend up to 300 dollars in total on these plants, we can write the equation as:

$1.2x + 2.5y = 300$

Answer for Part (a)

The equation that models the possible combinations of $x$ vinca plants and $y$ phlox plants is:

$1.2x + 2.5y = 300$

Answer for Part (b)

To graph this equation, you would typically rearrange it into slope-intercept form or plot the intercepts. Here’s a quick way to find intercepts:

1. To find the $x$-intercept (when $y = 0$): $1.2x = 300 \Rightarrow x = \frac{300}{1.2} = 250$

2. To find the $y$-intercept (when $x = 0$): $2.5y = 300 \Rightarrow y = \frac{300}{2.5} = 120$

So, the line would pass through points $(250, 0)$ and $(0, 120)$ on the graph.

Would you like a graph of this equation or further details on interpreting it?

Related Questions

1. How can you find other possible combinations of vinca and phlox plants within the budget?
2. What if the price of vinca or phlox plants changed? How would that impact the equation?
3. How would you determine the maximum number of one type of plant if only one type were purchased?
4. Can you rewrite the equation in slope-intercept form to understand the rate of trade-off between vinca and phlox plants?
5. What does each intercept represent in the context of this problem?

Tip

When solving for intercepts, setting one variable to zero simplifies the process and provides clear points for graphing linear equations.