an athletic department

An athletic department sold 454 tickets to a sporting event. Adults paid $3.50 per ticket, and students paid $1.00. The total tickets sales were $1,154. How many adults tickets and how many student tickets were sold to the event?

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Call the number of adult tickets sold "x" and the number of student tickets sold "y."

Then the number sold ....x + y = 454

And the revenue is equal to the cost of the adult ticket times the number of those sold plus the the cost of a student ticket times the number of those sold. In math terms, we have .....3.50x + 1.00y = 1154.....this gives the following system...

x + y = 454

3.5x + 1y = 1154    

Subtracting the first equation from the second, we have

2.5x = 700              

divide by 2.5 on each side   this gives

x = 280 = number of adult tickets sold

And the number of student tickets sold =  [454 - 280] = 174

Make sure you check these answers in both equations to see that they "work."