To find how many tickets of each type were sold, write one equation for the total number of tickets and a second for the total revenue. Use the same variables in both equations so the counts match the prices.
The 2027 SEC G3 Mathematics K310 syllabus covers simultaneous linear equations. This example shows how elimination works and how to spot a revenue figure that could not have come from whole-ticket sales.
- Define each variable in tickets.
- Write the count and revenue equations.
- Eliminate one variable.
- Check both totals.
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Label the numbers before forming equations
A concert sells 80 tickets. Adult tickets cost $9 and child tickets cost $5. Total ticket revenue is $584. Let a be the adult count and c the child count. The count equation is a + c = 80. The revenue equation is 9a + 5c = 584. The first equation is in tickets and the second is in dollars.
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Worked example | Eliminate the child count
Multiply the count equation by 5 to obtain 5a + 5c = 400. Subtract it from the revenue equation to get 4a = 184. This gives a = 46. Then c = 80 − 46 = 34. Check the count with 46 + 34 = 80 and the revenue with 46 × $9 + 34 × $5 = $584.
The same calculation has a practical meaning. If all 80 tickets were child tickets, revenue would be $400. Every adult ticket in place of a child ticket adds $4. The extra $184 therefore accounts for 46 adult tickets.
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Check whether the numbers are possible
Suppose the revenue is given as $585 and every ticket was sold at its stated price. The extra revenue over $400 would be $185. It is not a multiple of $4, so no whole-number ticket counts fit all the conditions. Rounding the result would change the revenue.
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Frequently asked questions
Can I use substitution instead?
Yes. Replace c with 80 − a in the revenue equation. Simplifying gives 4a + 400 = 584.
What can a parent ask when a child gets stuck?
Ask what the $400 represents in the example. Then ask how revenue changes when one child ticket is replaced with one adult ticket.