for a particular event, 812 tickets were sold for a total of $1912. If students paid $2 per ticket and nonstudents paid $3 per ticket, how many students tickets were sold?
S+N=812
2S+3N=1912
I assume that helps you. Solve by any method, I recommend substitution.
Let's assume the number of student tickets sold as 'S' and the number of non-student tickets sold as 'N'.
According to the given information:
S + N = 812 (equation 1) -- (Since the total number of tickets sold is 812)
2S + 3N = 1912 (equation 2) -- (Since students paid $2 per ticket and non-students paid $3 per ticket)
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 have:
N = 812 - S
Substituting this value into equation 2:
2S + 3(812 - S) = 1912
2S + 2436 - 3S = 1912
2436 - 1912 = 3S - 2S
524 = S
Therefore, the number of student tickets sold is 524.
To find the number of student tickets sold, let's assume "x" represents the number of student tickets sold.
The price for each student ticket is given as $2, so the total revenue from student ticket sales is 2x dollars.
The total number of tickets sold for the event is given as 812, which includes both student and nonstudent tickets. So, we can write an equation:
x + (total number of nonstudent tickets) = 812
The revenue from nonstudent ticket sales is calculated by subtracting the revenue from student ticket sales ($2x) from the total revenue of $1912:
1912 - 2x (nonstudent ticket revenue)
Now, let's solve the equation to find the value of "x," representing the number of student tickets sold:
x + 1912 - 2x = 812
Combining like terms:
1912 - x = 812
To solve for "x," let's isolate the variable by subtracting 812 from both sides of the equation:
1912 - 812 - x = 812 - 812
1100 - x = 0
Next, let's isolate "x" by subtracting 1100 from both sides of the equation:
1100 - x - 1100 = 0 - 1100
-x = -1100
To solve for "x," multiply both sides of the equation by -1:
-x * (-1) = -1100 * (-1)
x = 1100
Therefore, the number of student tickets sold for the event is 1100.