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

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.

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