Question

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?

Answer 1

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

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 2

240 = no. of $12 tickets

610 = no. of $8 tickets

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