Answer: $4.28
Explanation:
We can set up the following equation to find the cost of the admission of play:
(14 students x $2x admission) + (14 students x $2 program) = (22 students x $x admission) + (22 students x $4 program)
We know the admission cost for the play is twice that of the musical, so we can substitute that into the equation:
(14 students x $2x admission) + (14 students x $2 program) = (22 students x ($2x/2) admission) + (22 students x $4 program)
Simplifying the equation:
28x + 28 = 22x + 88
Solving for x:
28x + 28 = 22x + 88
28x - 22x = 88 - 28
6x = 60
x = 60/6
So, x = 10 is the solution of the equation.
And I got $2.14 from x = 60/28 = 2.14
That was the value that makes the equation true in the first step (14 students x $2x admission) + (14 students x $2 program) = (22 students x $x admission) + (22 students x $4 program)
So x = 2.14 is the price of the musical admission.
x = $2.14
Therefore, the admission cost for each student that is going to the play is $2x = $2.14 x 2 = $4.28.