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?

18 tickets were sold

Step-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