SOLUTION: You are buying movie passes and gift certificates as prizes for an event. You need at least 5 movie passes and 2 gift certificates. A movie pass costs $6 and a gift certificate cos

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Question 1118568: You are buying movie passes and gift certificates as prizes for an event. You need at least 5 movie passes and 2 gift certificates. A movie pass costs $6 and a gift certificate cost $10. The most you can spend is $70.
a) Write a system of linear inequalities that shoes the number of movie passes x and gift certificates y that can be purchased.
b) Graph the system
c) Use the graph to determine if you can buy 6 movie passes and 3 gift certificates.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
let x = number of movie passes.
let y = number of gift certificates.

you need at least 5 movie passes, so x >= 5.

you need at least 2 gift certificates, so y >= 2.

a movie pass costs 6 dollars and a gift certificate costs 10 dollars and the most ou can spend is 70 dollars, so 6x + 10y <= 70.

your system of requirements are:

x >= 5
y >= 2
6x + 10y <= 70

when x = 6 and y = 3, 6x + 10y <= 70 becomes 6*6 + 10*3 <= 70 which becomes 36 + 30 <= 70 which becomes 66 <= 70 which is true.

therefore, you can buy 6 movie passes and 3 gift certificates and still stay under the limit of 70 dollars.

the following graph shows that.

in this graph, the opposite of the constraint inequalities are graphed.

the area of the graph that is not shaded is the region of feasibility.

6 movie passes and 3 gift certificates is the intersection of the line x = 6 and y = 3.

that intersection is in the portion of the graph that is not shaded.

this means that 6 movie passes and 3 gift certificates are within the constraints of the problem.

this was shown algebraically above the graph.