at the concert, seated tickets cost M and standing tickets cost N. The seated tickets are three times the price of a standing ticket. If 200 seating tickets are sold and 100 standing tickets and the total receipts from the concert is $2100, find the price of seated ticket.
m=3n
200 m + 100 n = 2100
so
200(3n) + 100 n = 2100
700 n = 2100
n = 3
so m = 3n = 9
To find the price of the seated ticket, let's first set up equations based on the given information:
Let M be the price of a seated ticket.
Let N be the price of a standing ticket.
We know that the seated tickets are three times the price of a standing ticket, so we can write the equation:
M = 3N (equation 1)
We also know that 200 seating tickets are sold and 100 standing tickets, and the total receipts from the concert is $2100. The total receipts can be calculated by multiplying the number of each type of ticket sold by their respective prices and adding them together. So we can write the equation:
200M + 100N = 2100 (equation 2)
Now, we have a system of two equations (equation 1 and equation 2) with two variables (M and N). We can solve this system of equations to find the values of M and N.
Substitute equation 1 into equation 2:
200(3N) + 100N = 2100
Simplify:
600N + 100N = 2100
700N = 2100
N = 2100/700
N = 3
Now substitute the value of N back into equation 1 to find the value of M:
M = 3(3)
M = 9
Therefore, the price of a seated ticket is $9.