The price of admission for a concert was $9 for adults and $4 for children. Altogether, 1770 tickets were sold, and the resulting revenue was $14,680. How many adults and how many children attended the concert?
adult tickets sold --- x
children tickets sold --- 1770-x
solve: 9x + 4(1770-x) = 14680
Smelly Dolphins
Adult 1520
Children 250
To find out how many adults and children attended the concert, we can set up a system of equations based on the given information.
Let's assume the number of adults is A and the number of children is C.
From the first piece of information, we know that the price of admission for adults is $9, and for children, it is $4. Thus, the total revenue from adult tickets can be calculated as 9A, and from child tickets, it can be calculated as 4C.
The second piece of information tells us that the total number of tickets sold was 1770. Therefore, we can write the first equation as:
A + C = 1770
The third piece of information tells us that the total revenue from the ticket sales was $14,680. So, the second equation can be written as:
9A + 4C = 14,680
We now have a system of equations:
A + C = 1770 (Equation 1)
9A + 4C = 14,680 (Equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve the system of equations using the method of substitution:
Step 1: Solve Equation 1 for A in terms of C:
A = 1770 - C
Step 2: Substitute the value of A in Equation 2:
9(1770 - C) + 4C = 14680
Step 3: Simplify and solve for C:
15930 - 9C + 4C = 14680
-5C = -1250
C = 250
Step 4: Substitute the value of C back into Equation 1 to solve for A:
A = 1770 - 250
A = 1520
Therefore, there were 1520 adults and 250 children who attended the concert.