A total of 28 tickets for the summer fair were sold. A child ticket costs $2.50 and an adult ticket costs $3.75. If the total cost of the tickets sold is $82.50, how many child tickets were sold?
Accepted Solution
A:
Answer:18 tickets were soldStep-by-step explanation:The sum of the child tickets, C, and the adult tickets, A, is 28. Stated algebraically:
C+A=28
The cost per child’s ticket is $2.50 and the cost per adult’s ticket is $3.75, and the total cost was $82.50. Stated algebraically:
2.5C+3.75A=82.5
Multiply the first equation by −3.75 and use the method of elimination to directly solve for C:
−3.75C−3.75A=−105, which can be added to the second equation in order to eliminate the C variable:
2.5C+(−3.75C)+3.75A+(−3.75A)=82.5+(−105), which becomes:
−1.25C=−22.5, so C=18