Tickets to the school musical cost $3 for students and $5 for non students. Total ticket sales were $1790. The number of student tickets sold was 100 less than twice the number of non student tickets sold.
Write a system of equations to represent this situation. Solve the system of equations. How many student tickets sold? How many non students?
3s+5n = 1790
s = 2n-100
(s,n) = (190,280)
5n + 3n = 1790
n= tickets sold for non student
2n-100 = tickets sold for student
So,
5n + 3(2n-100)= 1790
5n + 6n - 300 = 1790
11n = 1790+300
11n= 2090
n= 190
So, substituting the value of n we 5(190)+ 3(2(190)-100) =1790
950 + 840 =1790
To represent this situation, we can create a system of equations using the given information:
Let's express the number of student tickets sold as "x" and the number of non-student tickets sold as "y".
Equation 1: The total ticket sales were $1790:
3x + 5y = 1790
Equation 2: The number of student tickets sold was 100 less than twice the number of non-student tickets sold:
x = 2y - 100
Now, let's solve this system of equations to determine the values of x (number of student tickets sold) and y (number of non-student tickets sold).
To solve this system, we can use either the substitution method or the elimination method. In this case, let's use the substitution method:
First, we can substitute the value of "x" from Equation 2 into Equation 1:
3(2y - 100) + 5y = 1790
Simplifying the equation by distributing the 3:
6y - 300 + 5y = 1790
Combining like terms:
11y - 300 = 1790
Adding 300 to both sides of the equation:
11y = 2090
Dividing both sides of the equation by 11:
y = 190
Now that we have the value of "y," we can substitute it back into Equation 2 to find the value of "x":
x = 2(190) - 100
x = 380 - 100
x = 280
Therefore, the number of student tickets sold is 280, and the number of non-student tickets sold is 190.