You are selling tickets for a new college play: "A Handful of Math Miracles". Student tickets cost $4 and general admission tickets cost $6. You sell 525 tickets and collect $2876. How many of each type of ticket did you sell?

York 2021-01-06 Answered

You are selling tickets for a new college play: "A Handful of Math Miracles". Student tickets cost $4 and general admission tickets cost $6. You sell 525 tickets and collect $2876.
How many of each type of ticket did you sell?
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Expert Answer

hosentak
Answered 2021-01-07 Author has 100 answers

Step 1
Consider the number of student tickets sold be x and the number of general admission tickets sold be y.
It is given that each student’s ticket cost is $4 and each general admission’s ticket cost is $6. The number of tickets sold is 525 and the amount collected is $2876.
According to the question, the equations are formed as
x+y=525 and 4x+6y=2876

Step 2
Solve the equations in order to find the values of x and y as follows.
4x+6(525x)=2876(y=525x)
4x+31506x=2876
2x=274
x=137
Step 3
Solve for y by substituting the value of x as follows.
137+y=525(x=137)
y=525137
y=388
Step 4
Check whether the values are correct or not.
4(137)+6(388)=2876
548+2328=2876
2876=2876(True)
Step 5
As the values for x and y satisfy the equations, the values of x and y are 137 and 388, respectively.
Therefore, the number of student tickets sold is 137 and the number of general admission tickets sold is 388.

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