1Cademy - Solving a Science Center Ticket Mixture Application

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Setting Up a Mixture Application Using a System of Equations

Example

Solving a Science Center Ticket Mixture Application

Apply the system of equations method to solve a ticket mixture application.

Problem: A science center sold $1{,}363$ tickets on a busy weekend. The receipts totaled $\$12{,}146$ . How many $\$12$ adult tickets and how many $\$7$ child tickets were sold?

Name the unknowns. Let $a =$ the number of adult tickets and $c =$ the number of child tickets.
Translate into a system of equations.

The total number of tickets sold is $1{,}363$ : $a + c = 1{,}363$
The total value of adult tickets is $12a$ and the total value of child tickets is $7c$ . The total receipts are $\$12{,}146$ : $12a + 7c = 12{,}146$ The system of equations is: $a + c = 1{,}363$ $12a + 7c = 12{,}146$

Solve the system using the elimination method. Multiply the first equation by $-7$ : $-7(a + c) = -7(1{,}363)$ $-7a - 7c = -9{,}541$ Add this to the second equation: $12a + 7c = 12{,}146$ $5a = 2{,}605$ $a = 521$ Substitute $a = 521$ into the first equation: $521 + c = 1{,}363$ $c = 842$
Check the result. $521$ adult tickets at $\$12$ each is $\$6{,}252$ . $842$ child tickets at $\$7$ each is $\$5{,}894$ . $6{,}252 + 5{,}894 = 12{,}146$ $\checkmark$
Answer the question. The science center sold $521$ adult tickets and $842$ child tickets.

Updated 2026-05-25

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OpenStax Intermediate Algebra

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