The cost of buying x feet of cedar and y feet of pine can be expressed as 2.5x+1.75y.
Inequality: 2.5x+1.75y ≤ 200 Graph:
Example amounts: 10 feet of cedar and 20 feet of pine, 30 feet of cedar and 20 feet of pine, and 10 feet of cedar and 60 feet of pine.
Practice makes perfect
We will write an inequality, draw its graph, and give three possible amounts of each type of wood that can be bought within our budget.
Inequality
Cedar costs $2.50 per foot and pine costs $1.75 per foot. Let's write an expression to represent the cost of buying x feet of cedar and y feet of pine.
2.5 x+ 1.75y
Since our budget is $200, this expression must be less than or equal to200.
2.5x+1.75y ≤ 200
Graph
To graph the inequality, will first write its boundary line. To do so, we replace the inequality sign with an equals sign.
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Inequality & & Boundary Line [0.8em]
2.5x+1.75y ≤ 200 & & 2.5x+1.75y = 200
Let's find the intercepts of the line. We will find the x-intercept by substituting 0 for y.
The line also passes through the point (0,114.3). Now, we will plot and connect the obtained points. Note that neither the number of feet of pine nor the number of feet of cedar can be negative. Therefore, we will only graph for non-negative values of x and y. Since the inequality is not strict, the line will be solid.
Now we need to determine the half-plane we should shade. To do so, we will use a test point. If substituting the point into the inequality produces a true statement, we shade the region that contains the point. Otherwise, we shade the opposite region. For simplicity, we will use (0,0) as our test point.
Since the test point produced a true statement, we will shade the region that includes (0,0).
Possible Amounts
Finally, we will find three possible amounts of each type of wood that can be bought within our budget. To do so, we need to determine the coordinates of three points within the shaded area.
We found three possible amounts of each type of wood that can be bough with our budget.
&10feet of cedar and 20feet of pine
&30feet of cedar and 20feet of pine
&10feet of cedar and 60feet of pine
