SOLUTION: There are 100 seats in a cinema.some are luxury seats costing �2 the rest are ordinary seats costing �1 each. When the cinema is full the takings come to a total of �170 . How many

Question 971913: There are 100 seats in a cinema.some are luxury seats costing �2 the rest are ordinary seats costing �1 each. When the cinema is full the takings come to a total of �170 . How many seats are luxury

Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

Let the number of luxury seats be x.
Then the number of ordinary seats, using
ONE PART = TOTAL MINUS OTHER PART,
is 100-x.
                      taking     takings
Type       Number      from      from
 of          of        EACH       ALL
seat        seats      seat      seats
-------------------------------------------
luxury       x          �2       �2x
ordinary  100-x         �1       �1(100-x)
-------------------------------------------
TOTALS      100      -----       �1700

 The equation comes from the column on the right

  

   �2x + 1�(100-x) = �170
     
      2x + 100 - x = 170

           x + 100 = 170

                 x = 70 = the number of luxury seat.

The number of ordinary seats is 100-x or 100-70 or 30 ordinary seats.

Checking:  70 luxury seats took in �1400 and 30 ordinary seats took in �300
            That's 100 seats.
            And indeed �1400 + �300 = �1700
Edwin

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