Create one variable for peppers and create one for tomatoes.
Inequality: 4p+3t≤12 Graph:
Example Solutions: (1,1) and (4,0)
Practice makes perfect
We have been asked to write an inequality, graph the inequality, and find two solutions for this inequality. Let's investigate these tasks one at a time.
Write the Inequality
We know that each pound of peppers p costs $4 and each pound of tomatoes t costs $3. We will write an expression to represent their total cost.
4p+3t
We also know that our budget is $12. This means that the total cost must be less than or equal to 12. Now, we can express this with an inequality.
4p+3t≤12
Now that we have our boundary line, let's go ahead and graph it. Note, because our inequality is less than or equal to our boundary line must be kept solid.
Now we need to decide which side of the function should be shaded. We can test this by substituting any point into the inequality and seeing if it holds true. Let's try with (0,0).
The point (0,0) is a solution to the inequality, so we should shade the side of the function containing that point.
Finally, we need to consider the domain and range of the function. We cannot buy a negative number of tomatoes or peppers. Therefore, our solution set should be limited to the first quadrant.
Find Solutions
Since we cannot purchase a fraction of a pepper or tomato, our possible solutions are any integer coordinate pairs that lie within the shaded area of our graph. Two examples are (1,1) and (4,0).
These points represent the fact that we can, while staying within our budget, purchase 1 pepper and 1 tomato or 4 tomatoes and 0 peppers.
