Question 1171608
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x = number of advance tickets sold
y = number of same-day tickets sold
x and y are placeholders for nonnegative whole numbers


The first equation is x+y = 40 because the instructions state "there were 40 tickets sold in all". 


Let's solve for y to get y = 40-x. I subtracted x from both sides.


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1 advance ticket costs $35
x advance tickets cost 35x dollars
eg: if you sold x = 10 advance tickets then 35*x = 35*10 = 350 dollars is earned from these tickets alone


1 same-day ticket costs $30
y of these tickets costs 30y dollars 
eg: if you sold y = 20 same-day tickets then 30*y = 30*20 = 600 dollars is earned from these tickets alone


In total we have 35x+30y dollars earned from both types of tickets combined.


We're told that "The total amount paid for them was $1325" so 35x+30y = 1325 is the second equation.


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The system of equations we have is
y = 40-x
35x+30y = 1325



We can use substitution to solve
35x+30y = 1325


35x+30( y ) = 1325


35x+30( 40-x ) = 1325  .... y replaced with 40-x


35x+30( 40 ) + 30( -x ) = 1325 


35x+1200-30x = 1325 


5x+1200 = 1325 


5x+1200-1200 = 1325-1200 .... subtract 1200 from both sides

 
5x = 125


5x/5 = 125/5 .... dividing both sides by 5


x = 25


There were 25 advance tickets sold.


Use this to find y
y = 40-x


y = 40-25


y = 15


There were 15 same-day tickets sold.


As a check,
x+y = 25+15 = 40
helps show that 40 tickets were sold
This confirms the first equation.


And also,
35x = 35*25 = 875 dollars earned from advance tickets only
30y = 30*15 = 450 dollars earned from same-day tickets only
35x+30y = 875+450 = 1375 dollars earned in total
This confirms the second equation.


Since both equations have been satisfied, this confirms our answers.


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Answers: 
25 advance tickets sold
15 same-day tickets sold

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