SOLUTION: The owner the Old Fashion Movie House wants to divide his 1800-seat cinema into three sections, pit, house and balcony with tickets costing $20, $35, and $50 respectively. He wan

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: The owner the Old Fashion Movie House wants to divide his 1800-seat cinema into three sections, pit, house and balcony with tickets costing $20, $35, and $50 respectively. He wan      Log On


   

Question 1138607: The owner the Old Fashion Movie House wants to divide his 1800-seat cinema into
three sections, pit, house and balcony with tickets costing $20, $35, and $50 respectively.
He wants the sum seat places in pit and house to be 7 times that of balcony, and to earn $48,000
when all seats are sold out.
a. Derive a system of three equations showing the information given.
b. Using either 𝐂𝐫𝐚𝐦𝐞𝐫′
𝐬 𝐑𝐮𝐥𝐞 or 𝐈𝐧𝐯𝐞𝐫𝐬𝐞 𝐌𝐞𝐭𝐡𝐨𝐝, find how many of seats must he have in each
section?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Only a start -

p pit
h house
b balcony

system%28p%2Bh%2Bb=1800%2Cp%2Bh=7b%2C20p%2B35h%2B50b=48000%29

Divide revenue equation by 5:
4p%2B7h%2B10b=9600


System of Equations:
system%28p%2Bh%2Bb=1800%2Cp%2Bh-7b=0%2C4p%2B7h%2B10b=9600%29




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you may like to try https://matrix.reshish.com/cramer.php .

p = 1225
h = 350
b = 225