Question

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

Answer 1

help me on it please

Answer 2

but only 100 seats and 100 dollars worth of money

Answer 3

I have a solution but it's a little bit ugly, do you want me to show you what I did?

Answer 4

8 adults, 27 seniors, 65 children works.

Answer 5

yes please show me how it works

Answer 6

?

Answer 7

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

Answer 8

TY