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Question: Help with math problem please *10pts*?

Tickets for admission to a high school football game cost $3 for students and $5 for adults. During one game, $2995 was collected from the sale of 729 tickets.

a) Write and solve a system of linear equations to find the number of tickets sold to students and the number of tickets sold to adults.
b) Graph the system of linear equations. Use the graph to determine weather to answer part (a) is reasonable.

Please problems confuse me. Please show steps

Thanks in advance

Answer: First you are going to want to set up your parameters. In this case that would be the two extremes: all tickets were students(x) or all tickets were adults(y).
3x = 2995...this would mean that 998.33 student tickets would need to be sold to get 2995 in sales
5y = 2995...this would mean that 599 adult tickets would need to be sold to get 2995 in sales

Because the actual number of tickets sold (729) is in between the extremes (599 and 998.33), it means that there was some combination of tickets sold. To figure out how many tickets sold you will want to use the following equations:

3x + 5y = 2995 (this is for the sales profits)
x + y = 729 (this is for number of tickets sold)

Then you will solve for one variable ( I will solve for x in the simpler equation):

x = 729 - y

Then you will substitute this answer into the other equation and solve:

3 (729 - y) + 5y = 2995
2187 - 3y + 5y= 2995
2187 + 2y = 2995
2y = 808
y = 404

Then you will substitute your findings back into one equation to solve for x:

x + 404 = 729
x = 325

So you sold 325 student tickets and 404 adult tickets. To make sure you're correct, put these numbers in your other equation and make sure it works:

3(325) + 5(404) = 2995
975 + 2020 = 2995
2995 = 2995

Now you know you are correct. Unfortunately I cannot draw the graph for you, but if you create your graph and just plot your equations you should be golden. The linear equations you will want to use are the ones described above, but solved for y.

y = 729 - x
y = 599 - 3/5x

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