York

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? ### Answer & Explanation hosentak Skilled2021-01-07Added 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

Step 2
Solve the equations in order to find the values of x and y as follows.
$4x+6\left(525-x\right)=2876\left(\because y=525-x\right)$
$4x+3150-6x=2876$
$-2x=-274$
$x=137$
Step 3
Solve for y by substituting the value of x as follows.
$137+y=525\left(\because x=137\right)$
$y=525-137$
$y=388$
Step 4
Check whether the values are correct or not.
$4\left(137\right)+6\left(388\right)=2876$
$548+2328=2876$
$2876=2876$(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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