Question

Tickets to a show cost different for seniors, children, and adults. Adult tickets are twice as much as senior tickets. Two senior tickets plus one children’s ticket cost $17. Two children tickets plus one adult ticket cost $24. How much does one senior ticket cost?

Answer 1

1A + 2C = $24, or, since A = 2S, you can write this as

2S + 2C = $24

The difference between $17 and $24 is $7, so this must be the cost of a child's ticket. Subtract this from $17 and you get $10, which must be the cost of 2 Senior tickets. So the Senior ticket costs $5, and the Adult ticket must cost $10.

Therefore 1 Adult and 1 Senior ticket costs $15