Transportation An air cargo plane can transport as many as 15 regular shipping containers. One super-size container takes up the space of 3 regular containers.
Write an inequality to model the number of regular and super size containers the plane can transport.
Describe the domain and range.
Graph the inequality you wrote in part (a).
Let x be the number of regular containers and y be the number of super-size containers.
The inequality to model the number of regular and super-size containers the plane can transport is:
x + 3y ≤ 15
Domain: The number of regular containers (x) can be any non-negative integer (x ≥ 0) and the number of super-size containers (y) can also be any non-negative integer (y ≥ 0).
Range: The sum of the number of regular containers and three times the number of super-size containers must be less than or equal to 15.
To graph the inequality x + 3y ≤ 15, we will plot the points (0, 5), (5, 3), (10, 0) on a coordinate plane and draw a line connecting these points. The line will be solid because the inequality includes equal to. Finally, shade the region below the line to represent the valid solutions or points (x, y) that satisfy the inequality.
Here is the graph of the inequality x + 3y ≤ 15:
(Note: This graph is a rough representation and may not be to scale)
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(10,0) |
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(5,3) |
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(0,5)------------------
0 5 10 15