Tickets for a school concert cost $9 for students and $15 for adults. In all 420 tickets were sold and the takings came to $4,860. How many student tickets were sold?

1. Let s be the number of student tickets and a the number of adult tickets. 2. The count gives s + a = 420, and the takings give 9s + 15a = 4860. 3. Rearrange the first rule to a = 420 - s. 4. Put that into the second rule: 9s + 15(420 - s) = 4860. 5. Expand to get 9s + 6300 - 15s = 4860, which tidies to 6300 - 6s = 4860. 6. Take 6300 from both sides to get minus 6s equals minus 1440, so s = 240 and a = 180. 7. Check the takings: 9 dollars times 240 is 2,160 dollars, and 15 dollars times 180 is 2,700 dollars, which add to 4,860 dollars. 8. Option B is the number of adult tickets, which is the easiest answer to hand in by mistake. 9. Option C gives takings of 1,800 dollars plus 3,300 dollars, which is 5,100 dollars, too much. 10. Option D gives takings of 2,340 dollars plus 2,400 dollars, which is 4,740 dollars, too little. _Source: OpenStax College Algebra (CC BY 4.0), Ch 7 "Systems of Equations and Inequalities", section 7.1 Systems of Linear Equations: Two Variables_