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An amateur drama group hire a theatre for their production. They expect to sell all 850 tickets, some at $12 and the rest at $8. The group require the ticket sales to cover their $3760 production costs and to make a profit of $4000. If they are to exactly achieve this target and their expectations regarding ticket sales are correct how many of the 850 tickets should they charge $12 for and how many should they charge $8 for?

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Answer:

610 tickets for $8, and 240 tickets for $12.

Step-by-step explanation:

x + y = 850

8x + 12y = 7760

x = 850 - y

8(850-y) + 12y = 7760

6800 - 8y + 12y = 7760

4y = 960

y= 240

x + 240 = 850

x= 610

Answer:

240 = no. of $12 tickets

610 = no. of $8 tickets

Step-by-step explanation:

Let x = no. of $12 tickets

y = no. of $8 tickets

12x = income from selling x $12 tickets

8y = income from selling y $8 tickets

If they are to make a profit of 4000, then they need to have a total income from sales of $7760

So,  x + y = 850         and              12x + 8y = 7760

            y = 850 - x                         12x + 8(850 - x) = 7760

                                                       12x + 6800 - 8x = 7760

                                                          4x + 6800 = 7760

                                                                      4x = 960

                                                                        x = 240 = no. of $12 tickets

            y = 850 - 240

              = 610 = no. of $8 tickets

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