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Question 1205098: Devonte is throwing a party to watch the Stanley Cup Finals. He orders pizza that cost $11 each and cartons of wings that cost $9.99 each. With at least 34 people coming over, Devonte spends at least $72.96 and orders a minimum of 7 pizzas and cartons of wings.
Part A. Write a system of inequalities that describes this situation.
Part B. Graph the solution set and determine a possible number of pizza and cartons of wings he ordered for his party.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = number of pizzas.
y = number of cartons of wings.
you have two inequalities that need to be solved simultaneously.
they are:
x + y >= 7
11x + 9.99y >= 72.96
with the desmos.com calculator, you would graph the opposite of the inequalities.
the area on the graph that is not shaded is your region of feasibility.
the graph is shown below.
your corner points are the minimum number of x and y that satisfy the inequality.
the corner points are in (x,y) format and are equal to (0,7.303), (3,4), (7,0).
for example, at (0,7.303), x is equal to 0 and y is equal to 7.303).
the value of y is actually equal to 7.303303303.
the value on the graph is rounded to 3 decimal places.
at (0,7.303303303), the inequalities are satisfied because:
x + y >= 7 becomes 0 + 7.303 = 7.303 >= 7.
11x + 9.99y >= 72.96 becomes 0 + 9.99*7.303303303 = 72.96 >= 7.96.
the minimum number of pizzas and cartons of wings becomes:
0 pizzas and 8 cartons of wings.
3 pizzas and 4 cartons of wings.
7 pizzas and 0 cartons of wings.
any value of x and y on the graph that are not shaded are valid combinations.
0 pizzas and 8 cartons of wings cost 9.99 * 8 = 79.92 which is greater than or equal to 72.96.
3 pizzas and 4 cartons of wings cost 3 * 11 + 4 * 9.99 = 72.96 which is greater than or equa to 72.96.
7 pizzas and 0 cartons of wings cost 7 * 11 = 77 which is greater than or equal to 72.96.
all inequalities are satisfied.
x + y >= 7
11x + 9.99y >= 72.96
one possible combination is 3 pizzas and 4 cartons of wings that would cost 33 + 39.96 for a total of 72.96 which is greater than or equal to 72.96.
here's the graph.
as long as x + y >= 7 and 11x + 9.99y >= 72.96, the combination is valid.
for example, when x + y = 20, any combination of x and y would satisfy the inequality.
for example:
when x = 0 and y = 20, the total cost is 20 * 9.99 which is >= 72.96
when x = 20 and y = 0, the total cost is 20 * 11 which is >= 72.96
when x = 10 and y = 10, the total cost is 10 * 11 + 10 * 9.99 which is >= 72.96.
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