tickets to a museum cost $5 for general admission and $2 with student ID. On Friday night 200 tickets were sold for $625. How many general admissions tickets were sold.
G + S = 200 Therefore:
G = 200 - S
5G + 2S = 625
Substitute 200-S for G in second equation and solve for S. Insert that value into the first equation and solve for G. Check by inserting both values into the second equation.
To solve this problem, we can set up a system of equations. Let's use the variables G and S to represent the number of general admissions and student tickets sold, respectively.
According to the problem, we know the following information:
1) The price of a general admission ticket is $5.
2) The price of a student ticket is $2.
3) The total number of tickets sold is 200.
4) The total revenue from ticket sales is $625.
Using this information, we can create two equations:
Equation 1: G + S = 200 (since the total number of tickets sold is 200)
Equation 2: 5G + 2S = 625 (since the total revenue from ticket sales is $625)
To solve the system of equations, we can use substitution or elimination. Let's use substitution:
From Equation 1, we can express G in terms of S: G = 200 - S.
Substituting this value of G into Equation 2:
5(200 - S) + 2S = 625
Simplifying the equation:
1000 - 5S + 2S = 625
Combining like terms:
-3S + 1000 = 625
Subtracting 1000 from both sides:
-3S = -375
Dividing both sides by -3:
S = 125
Now that we have the number of student tickets sold (S = 125), we can substitute this value back into Equation 1 to find the number of general admissions tickets sold:
G + 125 = 200
Subtracting 125 from both sides:
G = 75
Therefore, 75 general admissions tickets were sold.