Tickets to see a movie is $16 for an adult and $10 for students. if they sold 400 tickets, which totaled $4,600, how many of each type did they sell?

Step-by-step explanation:

Let "a" represent the number of adult (highest price) tickets sold. Then 400-a is the number of student tickets, and the revenue is ...

  16a +10(400 -a) = 4600

  6a = 600 . . . . . . . . . . . . . . . simplify, subtract 4000

  a = 100 . . . . . . . . . . . . . . . . . divide by the coefficient of a

100 adult and 300 student tickets were sold.

Note that the above can be described by the verbal reasoning: If all the tickets sold were the (lower price) student tickets, revenue would be $4000. It was actually $600 more than that. Each adult ticket sells for $6 more than a student ticket, so there must have been $600/$6 = 100 adult tickets sold.

Another way to work this problem is as a "mixture" problem. The average selling price per ticket is $4600/400 = $11.50. The differences between this price and the adult and student ticket prices are 4.50 and 1.50, so the ratio of student tickets to adult tickets is 4.50:1.50 = 3:1. That is, there were 300 student tickets sold and 100 adult tickets sold.

e) none of the above because the measure of angle cba is 101°

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step-by-step explanation: