anonymous
  • anonymous
A cinema has 100 seats Show how it is possible to sell exactly 100 tickets and take in exactly $100 if the ticket prices are: Adults: $10 Seniors: 50 cents Children: 10 cents
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
help me on it please
anonymous
  • anonymous
but only 100 seats and 100 dollars worth of money
anonymous
  • anonymous
I have a solution but it's a little bit ugly, do you want me to show you what I did?

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anonymous
  • anonymous
8 adults, 27 seniors, 65 children works.
anonymous
  • anonymous
yes please show me how it works
anonymous
  • anonymous
?
anonymous
  • anonymous
10a+.5s+.1c=100 a+s+c=100 multiply the top by 10 100a+5s+c=1000 a+s+c=100 now subtract the second equation from the first: 99a+4s=900 so we start by choosing a so that when you take 900-99a the result is divisible by 4. Since 900 is divisible by 4 we want to subtract a multiple of 4 from it so we try a=4,8,etc. a=4 gives more than 100 for s so that doesnt work. try a=8: 900-99*8=900-792=108 4s=108 s=27 so a=8,s=27 a+s+c=100 so c=65. we can check to see if the revenue is 100 too: 8*10+27*.5+65*.1=80+13.5+6.5=100 so it checks out
anonymous
  • anonymous
TY

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