Question

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?

Math Word Problem
ANSWERED
asked 2021-01-06

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?

Answers (1)

2021-01-07

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.
\(4x+6(525-x)=2876 (\because y=525-x)\)
\(\displaystyle{4}{x}+{3150}-{6}{x}={2876}\)
\(\displaystyle-{2}{x}=-{274}\)
\(x=137\)
Step 3
Solve for y by substituting the value of x as follows.
\(137+y=525 (\because x=137)\)
\(y=525-137\)
\(y=388\)
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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