Tickets to a concert cost $12 for kids and $15 for adults. A total of 300 tickets were sold and total receipts were $4140. How many were adult tickets and how many kids?
adults -- x
kids --- 300-x
solve:
15x + 12(300-x) = 4140
180 and 120
Let's assume the number of adult tickets sold as 'x' and the number of kids' tickets sold as 'y'.
According to the given information:
1. The price of an adult ticket is $15.
2. The price of a kid's ticket is $12.
3. The total number of tickets sold is 300.
4. The total receipts from ticket sales are $4140.
We can create the following equations based on the given information:
Equation 1: x + y = 300 (Total number of tickets sold)
Equation 2: 15x + 12y = 4140 (Total receipts from ticket sales)
To solve these equations, we can use the method of substitution or elimination.
Let's solve using the method of substitution:
From Equation 1, we can express x in terms of y:
x = 300 - y
Substitute the value of x in Equation 2:
15(300 - y) + 12y = 4140
4500 - 15y + 12y = 4140
-3y = 4140 - 4500
-3y = -360
y = -360 / -3
y = 120
Now, substitute the value of y in Equation 1 to find x:
x + 120 = 300
x = 300 - 120
x = 180
Therefore, there were 180 adult tickets sold and 120 kids' tickets sold.
To solve this problem, let's represent the number of kids' tickets as 'k' and the number of adult tickets as 'a'.
Given that tickets for kids cost $12 and tickets for adults cost $15, we can set up the following equations:
1. k + a = 300 (since a total of 300 tickets were sold)
2. 12k + 15a = 4140 (since the total receipts were $4140)
To solve this system of equations, we can use a method called substitution.
From equation 1, we can express k in terms of a:
k = 300 - a
Substitute this value of k into equation 2:
12(300 - a) + 15a = 4140
Now, simplify and solve for a:
3600 - 12a + 15a = 4140
3a = 540
a = 180
So, there were 180 adult tickets sold.
Substituting this value of a back into equation 1:
k + 180 = 300
k = 300 - 180
k = 120
Therefore, there were 120 kids' tickets sold.
In summary, there were 180 adult tickets and 120 kids' tickets sold for the concert.