400 tickets were sold for a school play. General admission tickets were $4, and student tickets were $3. If the total ticket sales were $1323, how many student tickets were sold? I have been going over this and i cant seem to get the answer correct or to make sense
Hi Sara,
You have to create a system of equations.
First 3x+4y=1323
Second x+y=400
Now use substitution to solve
Can you take it from here?
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To solve this problem, we can set up a system of equations. Let's define two variables: G for the number of general admission tickets sold, and S for the number of student tickets sold.
According to the problem, 400 tickets were sold in total, so we can write the equation:
G + S = 400 (Equation 1)
We also know that the total ticket sales amount to $1323. The general admission tickets cost $4 each, so the revenue from these tickets is 4G. Similarly, the student tickets cost $3 each, so the revenue from these tickets is 3S. We can write the second equation:
4G + 3S = 1323 (Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) with two variables (G and S). We can solve this system to find the values of G and S.
One way to do this is to solve Equation 1 for G or S and then substitute it into Equation 2. Let's solve Equation 1 for G:
G = 400 - S
Now substitute G into Equation 2:
4(400 - S) + 3S = 1323
Let's simplify this equation:
1600 - 4S + 3S = 1323
1600 - S = 1323
-S = 1323 - 1600
-S = -277
If we multiply both sides of this equation by -1, the signs will change:
S = 277
Therefore, the number of student tickets sold is 277.