A ticket to a concert costs either $12 for a child or $15 for an adult. A total of 300 tickets are sold and the total money collected is $4140 . The number of child tickets sold is
a+c = 300
15a + 12c = 300
solve for c.
To find the number of child tickets sold, we need to set up a system of equations based on the given information.
Let's assume the number of child tickets sold is C and the number of adult tickets sold is A.
We know that the cost of a child ticket is $12 and the cost of an adult ticket is $15.
So, the total money collected from selling child tickets would be 12 * C, and the total money collected from selling adult tickets would be 15 * A.
According to the given information, the total money collected is $4140. This means we can write the equation:
12C + 15A = 4140
We also know that the total number of tickets sold is 300. So, we can write another equation:
C + A = 300
Now we have a system of two equations with two variables. We can solve this system to find the values of C and A.
First, let's solve the second equation for C:
C = 300 - A
Substitute this value of C into the first equation:
12(300 - A) + 15A = 4140
Expanding and simplifying the equation:
3600 - 12A + 15A = 4140
Combine like terms:
3A = 540
Divide both sides by 3:
A = 180
Now that we know the value of A, substitute it back into the second equation to find the value of C:
C + 180 = 300
C = 300 - 180
C = 120
Therefore, the number of child tickets sold is 120.