You want to purchase at least 10 tickets to a baseball game, but can spend at most $200. Lower level tickets &8 each, while upper level tickets cost $5. Write and graph a system of inequalities to represent the situation. Give two possible combinations of the number of lower level tickets and upper level tickets that you can purchase.
let the number of lower tickets be x
let the number of upper tickets be y
x+y ≥10 ---> y ≥ -x + 10
8x + 5y ≤ 200 ---> y ≤ - (8/5)x + 40
sketch both inequalities then pick any two points in their intersection.
To represent this situation, we can use the following system of inequalities:
Let x be the number of lower level tickets and y be the number of upper level tickets.
The cost of lower level tickets is $8 each, so the cost of x lower level tickets is 8x.
The cost of upper level tickets is $5 each, so the cost of y upper level tickets is 5y.
The total cost of the tickets should be at most $200, so we have the inequality:
8x + 5y ≤ 200
We also want to purchase at least 10 tickets, so the total number of tickets should be at least 10, leading to the inequality:
x + y ≥ 10
Graphically, the graph of the system of inequalities will be a region in the x-y plane that satisfies both conditions.
Now, let's find two possible combinations of the number of lower level tickets and upper level tickets that you can purchase:
Combination 1:
Let's assume you purchase x = 6 lower level tickets and y = 4 upper level tickets. The total cost would be:
8(6) + 5(4) = 48 + 20 = $68.
Combination 2:
Now, let's assume you purchase x = 8 lower level tickets and y = 2 upper level tickets. The total cost would be:
8(8) + 5(2) = 64 + 10 = $74.
These are two possible combinations that satisfy the given conditions.