Question 154505
We can use the given information to set up a system of equations and find each of the variables.


We were told that there were a total of 600 tickets sold:


x + y = 600


And that one type of ticket was sold for two dollars while the other type was sold for five dollars.  The total in sales was $1500.


2x + 5y = 1500


Now, we can manipulate the first equation to find x in terms of y.


x = 600 - y 


And plug this into the second equation in order to solve for y.


2( 600 - y ) + 5y = 1500
1200 - 2y + 5y = 1500
3y = 300
y = 100


We can plug this value into either of the two equations to find the value for x.


x + 100 = 600
x = 500


So there were 100 five dollar tickets sold and 500 two dollar tickets sold, but just to be certain, we can plug these values back into either equation to check our answer.


2( 500 ) + 5( 100 ) = 1500
1000 + 500 = 1500


Since this is true, we know that our answers are correct.