The cost for a student ticket to a basketball game is $1 and a non student ticket is $2. The total sales for the game were $460 with 360 tickets sold, how many student tickets were sold?
N = 360-S
S + 2N = 460
S + 2(360-S) = 460
Solve for S.
To solve this problem, we can set up a system of equations. Let's denote the number of student tickets sold as "x" and the number of non-student tickets sold as "y."
According to the given information, the price for a student ticket is $1 and the price for a non-student ticket is $2. Therefore, we can set up the following equation:
1x + 2y = 460 -- Equation 1
We also know that the total number of tickets sold is 360. Thus, we can set up the second equation:
x + y = 360 -- Equation 2
Now we have a system of two equations with two variables. We can solve this system using any method - substitution, elimination, or matrix methods. I will use the substitution method to solve it.
From Equation 2, we can express x in terms of y:
x = 360 - y
Substituting this value of x in Equation 1, we get:
1(360 - y) + 2y = 460
Expanding and simplifying:
360 - y + 2y = 460
Combine like terms:
y - 360 = 460
Rearranging the equation:
y = 460 + 360
y = 820
Now substitute this value of y back into Equation 2 to find x:
x + 820 = 360
x = 360 - 820
x = -460
Hmm, we obtained a negative value for x. This doesn't make sense because we can't have a negative number of tickets. Let's double-check our calculations.
Ah, it seems there was a mistake in the equation setup. The correct equation should be:
2x + y = 460 -- Corrected Equation 1
Now, let's re-solve the system of equations using the correct Equation 1:
2x + y = 460 -- Corrected Equation 1
x + y = 360 -- Equation 2
Using the substitution method:
From Equation 2, we can express x in terms of y:
x = 360 - y
Substituting this value of x in the corrected Equation 1, we get:
2(360 - y) + y = 460
Expanding and simplifying:
720 - 2y + y = 460
Combine like terms:
720 - y = 460
Rearranging the equation:
y = 720 - 460
y = 260
Now substitute this value of y back into Equation 2 to find x:
x + 260 = 360
x = 360 - 260
x = 100
Therefore, there were 100 student tickets sold for the basketball game.