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Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $65 . For one performance, 20 advance tickets and 30 same-day tickets were sold. The total amount paid for the tickets was $1700 . What was the price of each kind of ticket?

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GoddessofDork

Steps

So for this, we will create a system of equations. With our information given, these are our two equations (let x = advance and y = same-day):

[tex]x+y=65\\20x+30y=1700[/tex]

So for this system, I will be using the substitution method. With the first equation, subtract both sides by y:

[tex]x=65-y\\20x+30y=1700[/tex]

Now that we know that x is equal to 65 - y, substitute that into the second equation and solve for y:

[tex]20(65-y)+30y=1700\\1300-20y+30y=1700\\1300+10y=1700\\10y=400\\y=40[/tex]

Now that we know the value of y, substitute that into either equation to solve for x:

[tex]x+40=65\\x=25\\\\20x+30(40)=1700\\20x+1200=1700\\20x=500\\x=25[/tex]

Answer

In short:

  • Advance Tickets: $25
  • Same-Day Tickets: $40

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