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?
- 7 years agoFavorite 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.
- saladoLv 43 years ago
2x + 2y = 20 utilising the simultaneous technique 2x - 2y = 4 ____________ 4x = 24 ( divide by potential of four) x = 6 replace x in considered one of the two equations 2x + 2y = 20 2 (6) + 2y = 20 12 +2y = 20 2y = 20 - 12 2y = 8 (divide by potential of two) y = 4 answer : X = 6 , Y = 4