Question
Asked Sep 12, 2019

A 5000 seat theater has tickets for sale at 27$ and 40$. How many tickets should be sold at each price for a sellout performance to generate a total revenue or 151900?

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Step 1

Suppose that x be the number of tickets sold for $27 and y be the number of tickets sold for $40 respectively, to obtain the total revenue of $151900.

. 27x + 40y 151900..
. ...(1)
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. 27x + 40y 151900.. . ...(1)

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Step 2

Also, the total number of tickets sold for the sell-out performance is 5000.

x+y=5000....
(2)
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x+y=5000.... (2)

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Step 3

From (2), substitute y=5000-x ...

27x 405000 x) = 151900
27x 200000-40x =151900
27x-40x = 151900- 200000
or, 40x 27x = 200000 -151900
13x 48100
48100
13
x = 3700
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27x 405000 x) = 151900 27x 200000-40x =151900 27x-40x = 151900- 200000 or, 40x 27x = 200000 -151900 13x 48100 48100 13 x = 3700

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Algebra