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Question 328752: Can someone please walk me through this?
The receipts for one showing of a movie were $540 for an audience of 120 people. The ticket prices are given in the table. If twice as many children's tickets as general admission tickets were purchased, how many of each type of ticket were sold?
Ticket Prices
Children $4
General Admission $6
Seniors $4
___ children's tickets
___ general admission tickets
___ senior tickets
Thank you!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! The receipts for one showing of a movie were $540 for an audience of 120 people. The ticket prices are given in the table. If twice as many children tickets as general admission tickets were purchased, how many of each type of ticket were sold?
Ticket Prices
Children $4
General Admission $6
Seniors $4
Let c = number of children tickets
Let g = number of general admission tickets
Let s = number of senior tickets.
Total revenue = 4*c + 6*g + 4*s = 540
Total number of people attending = c + g + s = 120
Solve these 2 equations simultaneously and you should be able to find the number of c and g and s.
Only problem is you have 2 equations in 3 unknowns.
You need either 3 equations in 3 unknowns or 2 equations in 2 unknowns to get an exact solution.
Fortunately, they tell you a relationship that you can use to reduce the number of unknowns.
That relationship is that 2 times the number of children tickets sold was twice the number of general admission tickets sold.
In algebraic form, this means the c = 2*g
You can substitute for c in your equations to reduce the number of unknowns from 3 to 2.
Your equations were:
Total revenue = 4*c + 6*g + 4*s = 540
Total number of people attending = c + g + s = 120
Substitute 2*g for c in both of these equations to get:
4*2*g + 6*g + 4*s = 520
2*g + g + s = 120
Simplify and combine like terms to get:
14*g + 4*s = 520
3*g + s = 120
Now you have 2 equations in 2 unknowns that can be solved for a unique solution.
If you multiply the second equation by 4, then you will be able to subtract one equation from the other to get down to 1 unknown in 1 equation.
After multiplying the second equation by 4, you get:
14*g + 4*s = 520
12*g + 4*s = 480
Subtract the second equation from the first equation to get:
2*g = 40
Divide both sides of this equation by 2 to get:
g = 20
Since c = 2*g, this means that c = 40
You can substitute in either original equation to find s.
You had c + g + s = 120
Substitute to get 60 + s = 120
Solve for s to get s = 60
you now have c = 40, g = 20, s = 60
Confirm this solution is correct by substituting in the other original equation.
That equation is:
4*c + 6*g + 4*s = 540
Substituting, you get:
160 + 120 + 240 = 520 which is correct, confirming that your solution is good.
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