Question

Ticket Receipts Solve by setting up a system of linear equations with 2 variables and 2 unknowns. An overwhelmed concert manager realized the next day after a concert that 350 ticket receipts were counted. The price for a student ticket was $12.50 and the price for an adult ticket was $16.00. The register confirmed $5,075 was taken in, too. What the manager did not keep track of was the number of student tickets and the number of adult tickets that were sold. How many of each were sold? There were 175 student tickets and 175 adult tickets sold. There were 155 student tickets and 195 adult tickets sold. There were 125 student tickets and 225 adult tickets sold. There were 150 student tickets and 200 adult tickets sold.

Answer 1

There were 150 student tickets and 200 adult tickets sold

Explanation:

Let s and a represent the numbers of student and adult tickets sold, respectively. Then the two equations are ...

s + a = 350 . . . . . . total number of tickets sold

12.50s + 16.00a = 5075 . . . . . .total value of tickets sold

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Solution

The first equation lets us write an expression for s:

s = 350 - a

We can substitute this into the second equation:

12.50(350 -a) +16.00a = 5075

3.50a + 4375 = 5075 . . . . . . . . . simplify

3.50a = 700 . . . . . . . . . . . . . . . . . subtract 4375

a = 200 . . . . . . . . . . . . . . . . . . . . . divide by 3.50

There were 200 adult tickets and 150 student tickets sold.