Break Even Question Accounting Need Help

Question

Hitami Opera performs at a local theater. The average show sells 1,000 tickets at $60 per ticket. The company runs 80 shows a year and each show requires a team of 75 artists. Each artist receives a base salary of $10,000 per year plus $375 per show. Program printing cost is $2 per guest. Sales commission to agent includes a base of $2,000 per show plus a commission of $3 per ticket. Annual rent and other fixed costs total $300,000. The number of shows that must be performed each year to break even is? (Round to nearest whole #)

A) 60 shows B) 50 shows C) 42 shows D) 34 shows E) Correct Answer Not Listed

 

Answer was 42 shows but I need help as to how with steps.

Answer 1

revenue is $60,000 per show.  (1000 tickets @ $60 per ticket)

Let's call the number of shows "x"

Disregard the 80 shows per year because the question asks how many shows needed to break even.

 

cost is more complicated.

salaries are $750,000 + 375(75)x     (75 artists x 10,000 per year + 375 each artist, each show "x")

program printing is $2000x  ($2 for 1000 tickets each show times "x" number of shows)

commission is $2000x + $3000x   ($2000 per show "x" and $3 per ticket (1000 each show) times number of shows "x")

rent and fixed costs $300,000 per year

 

equation:

$60,000x = $750,000+ $300,000 + (375)(75)(x) + 2000x + 2000x + 3000x

simplify

60,000x = 1,050,000 + 35125x

24,875x = 1,050,000

x = 42.211 

round to nearest whole number:  42 shows.