Possible Amounts: 6 pounds of cod and 8 pounds of flounder, 10 pounds of cod and 10 pounds of flounder, 12 pounds of cod and 3 pounds of flounder
Practice makes perfect
In this exercise we will write an inequality to represent fish sales. We have been told that the fish market charges $9 per pound for cod and $12 per pound for flounder. Let x be the number of pounds of cod and y be the number of pounds of flounder. Notice that the daily quota is at least $120.
Verbal Expression
Algebraic Expression
Cost of x pounds of cod ($)
9x
Cost of y pounds of flounder ($)
12y
Total cost of the fish ($)
9x+ 12y
Minimum daily quota is $120
9 x+ 12 y≥ 120
As a result we get an inequality that will help help the fish market determine how to reach their daily quota.
9x+12y≥120
Next, let's graph the inequality.
Graph of the Inequality
In order to graph the inequality, we will start by isolating y.
Now we will graph the inequality. In order to do that we need to determine the boundary line. We can do this by replacing the inequality symbol with an equals sign.
Inequality & Boundary Line
y ≥ -3/4x+10 & y = -3/4x+10
The boundary line is already in the slope-intercept form, y= mx+ b,
where m is the slope and b is the y-intercept. Therefore, we can plot the y-intercept and find a second point in order to draw the line. Notice that the inequality is not strict, so the line will be solid.
Next, we will choose an arbitrary point. If the point satisfies the inequality, we will shade the region that contains the point. Otherwise, we will shade the other region. Let's choose the point (0,0).
Since the point does not satisfy the inequality, we will not shade the region that contains the point. Notice that we will only shade values contained in the first quadrant because we cannot have a negative number of fish.
Next, we will determine three possible amounts each fish.
Possible Amounts of Fish
Any whole number values in the shaded region will satisfy the inequality. Thus, the three possible amounts of each fish are the following.
