Question

You are manning the ticket box for the community theater. You have sold a total of 201 tickets. Adult tickets to the show cost $18 senior tickets cost $15, and a child's ticket costs $8. The total amount you have collected is $2967. You also know you have sold twice as many adult tickets as children's tickets.
1. Write a system of equations in standard form to model this situation.

2. Create a matrix equation.

3. Solve the matrix equation.

4. How many of each type of ticket have you sold?


Please help I don't understand!​

Answer 1

You sold 96 adult tickets, 48 child tickets, and 15 senior tickets.

Since you are manning the ticket box for the community theater, and you have sold a total of 201 tickets, and adult tickets to the show cost $ 18, senior tickets cost $ 15, and a child's ticket costs $ 8, and the total amount you have. collected is $ 2967, you also know you have sold twice as many adult tickets as children's tickets, to determine how many of each type of ticket have you sold the following calculation must be performed:

• 100 x 18 + 50 x 8 + 51 x 15 = 2965
• 102 x 18 + 51 x 8 + 48 x 15 = 2964
• 96 x 18 + 48 x 8 + 57 x 15 = 2967

Therefore, you sold 96 adult tickets, 48 child tickets, and 15 senior tickets.

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