Sold 550 total tickets and collected $9200. Adult ticket costs $20 and child ticket costs $8. How much of each ticket type did they sell?

Question

how do I write the equation to get the answer?

 

Answer 1

The total number of tickets is the sum of adult tickets and child tickets sold.

 

A + C = 550

 

The total income is the sum of the income from adult tickets and from child tickets.

 

A*20 + C*8 = 9200

 

Solve for A from the first equation

 

A = 550 - C

 

Substitute A in the second equation

 

(550 - C)*20 +C*8 = 9200

 

Solve for C

 

C = 150

 

Substitute the solution for C in the first equation.

 

A + 150 = 550

 

Solve for A

 

A = 300

 

Final result:

 

300 adult tickets sold

150 child tickets sold