While browsing at her local farmers' market, Lexi stops at a booth selling fancy candles and hand soaps. She has $50 to spend. Candles cost $12.50 each, and hand soaps cost $5 each.
Graph the inequality that represents how many candles, x, and hand soaps, y, Lexi can buy.
Plot points on the boundary line. Select the line to switch between solid and dotted. Select a region to shade it.
The inequality representing how many candles and hand soaps Lexi can buy is:
$$12.5x + 5y \leq 50$$
Let's graph this inequality.
First, let's find the intercepts:
- For candles (x-intercept): Set y = 0
$$12.5x + 5(0) = 50$$
$$12.5x = 50$$
$$x = 4$$
- For hand soaps (y-intercept): Set x = 0
$$12.5(0) + 5y = 50$$
$$5y = 50$$
$$y = 10$$
Plotting these intercepts on the graph:
The x-intercept is at (4,0) and the y-intercept is at (0,10).
Now let's draw the boundary line by connecting these two points.
The boundary line is:
$$12.5x + 5y = 50$$
Next, let's shade the feasible region. To do this, we can pick a test point such as the origin (0,0) and substitute it into the inequality:
$$12.5(0) + 5(0) \leq 50$$
$$0 \leq 50$$
Since the inequality is true, the origin (0,0) is in the feasible region. We shade the region below the boundary line.
The resulting graph shows the shaded feasible region where Lexi can buy candles and hand soaps within her budget of $50.