Question

a high school play costs an up front $3000 to produce plus an additional cost of each performance. Every sold-out performance of the play brings in $2500 of revenue to the school. how many sold out performances are needed so that the school breaks even on the production of the play

Answer 1

So based on the information here, it costs $3,000 up front but an additional $1,000 for each play and each sold out performance brings in $2,500

For the sake of simplicity, when solving it, I won't be putting the dollar sign

So the equation is the following:

3,000+1,000x=2,500x 

So you need to get "x" by itself

First, minus 1,000x from each side

So it is now 3,000=1,500x

Now you divide 3,000 by 1,500 which is 2

x=2

So that means two performances need to sell out in order to break even with the cost

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To check:

$3,000+$1,000(2)=$2,500(2)

$1,000×2=$2,000 and $3,000+$2,000=$5,000

$5,000=$2,5000(2)

$2,500×2=$5,000

$5,000=$5,000

So it it correct