Mike asked in Science & MathematicsMathematics · 7 years ago

# Help solving math problem?

A theater hosted a small concert, offering only reserved seating. Covered resered seats were sold for a $50 donation, while uncovered reserved seats were sold for a$20 donation. The total number of seats sold was 725, with total ticket sales of $23,500. How many of each type of ticket did the theater sell? ### 2 Answers Relevance • 7 years ago Favorite Answer Let c = number of covered seats sold, u = number of uncovered seats sold. First write the cost equation. 50c + 20u = 23500 This shows that$50 per covered seat sold, plus $20 per uncovered seat sold, totals$23500.

Now write the sales equation.

c + u = 725

This shows that the total number of covered and uncovered seats sold totals 725. Rewrite the equation with one variable by itself.

c = 725 - u

Now substitute (725-u) for c in the cost equation.

50(725-u) + 20u = 23500

36250 - 50u + 20u = 23500

36250 - 30u = 23500

-30u = -12750

u = 425

There were 425 uncovered seats sold. Now substitute 425 for u in the sales equation.

c = 725 - 425

c = 300

There were 300 covered seats sold.