Tickets to a game are $5 for adults and $2 for children. Six hundred tickets are sold for a total of $2160. How many adult tickets and how many children's tickets have been sold?
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Sorry, shared computer at school, but can you help???
To solve this problem, we can use a system of equations. Let's denote the number of adult tickets as 'A' and the number of children's tickets as 'C'.
The first equation we can form is based on the total number of tickets sold: A + C = 600.
The second equation can be formed based on the total revenue generated: 5A + 2C = 2160.
To solve this system of equations, we can use the method of substitution. Let's solve the first equation for A and substitute it into the second equation:
A = 600 - C
Substituting A in the second equation:
5(600 - C) + 2C = 2160
3000 - 5C + 2C = 2160
-3C = 2160 - 3000
-3C = -840
C = -840 / -3
C = 280
Now that we have the value for C, we can substitute it back into the first equation to find A:
A + 280 = 600
A = 600 - 280
A = 320
Therefore, 320 adult tickets and 280 children's tickets have been sold.