Entertainment The map shows the number of tickets needed for small or large rides at the fair. You do not want to spend more than $15 on tickets. How many small or large rides can you ride?
You can buy 60 tickets with $15.
Relate | the number of tickets for small rides | plus | the number of tickets for large rides | is less than or equal to | 60 | ||||
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Define |
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Write | 3x | + | 5y | ≤ | 60 |
What are the unknowns?
The unknowns are the number of small rides and the number of large rides you can get on.
Step 1
Find the intercepts of the boundary line. Use the intercepts to graph the boundary line.
Graph the line that connects the intercepts (20, 0) and (0, 12). Since the inequality is
Step 2
The region above the boundary line represents combinations of rides that require more than 60 tickets. You purchased a finite number of tickets, 60, so you will not be able to go on an infinite number of rides. Shade the region below the boundary line.
The number of small rides x and the number of large rides y are whole numbers. In math, such a situation is called discrete. All points with whole number coordinates in the shaded region represent possible combinations of small and large rides.