tickets for a school play cost $4 for adults and $2 for students at the end of the play the school sold a total of 105 tickets and collected $360 how much of each type of tickets did they sell .
A = 105 - S
4A + 2S = 360
Substitute 105-S for A in the second equation and solve for S. Insert that value into the first equation to solve for A. Check by putting both values into the second equation.
To solve this problem, we can use a system of equations. Let's represent the number of adult tickets sold as 'A' and the number of student tickets sold as 'S'.
From the given information, we can set up the following equations:
Equation 1: A + S = 105 (the total number of tickets sold is 105)
Equation 2: 4A + 2S = 360 (the total amount collected from ticket sales is $360)
To solve this system of equations, we can use a method called substitution:
1. Solve Equation 1 for one variable (let's solve it for A):
A = 105 - S
2. Substitute the value of A obtained from Equation 1 into Equation 2:
4(105 - S) + 2S = 360
Simplify and solve for S:
420 - 4S + 2S = 360
-2S = 360 - 420
-2S = -60
S = -60 / -2
S = 30
Now that we have the value for S, we can substitute it back into Equation 1 to find A:
A = 105 - S
A = 105 - 30
A = 75
So, the school sold 75 adult tickets and 30 student tickets.