Question

32,000 people attended a ballgame at a stadium that offers two kinds of seats: general admission and reserved. The day's receipts were $200,000. How many people paid $13.00 for reserved seats, and how many paid $4.00 for general admission?

Answer 1

Let x = the number of reserved seats sold and y = the number of general seats sold.
1) x+y = 41,000 "41,000 people attended..."
2) $14(x)+$5(y) = $340,000 "The day's receipts were $340,000."
Rewrite equation 1) as x = y-41,000 and substitute into equation 2)
2a) 14(41,000-y)+5y = 340,000 Simplify and solve for y.
2a) 574,000-14y+5y = 340,000 Combine the y-terms.
2a) 574,000-9y = 340,000 Subtract 574,000 from both sides.
-9y = -234,000 Divide both sides by -9.
y = 26,000 and...
x = 41,000-26,000
x = 15,000
15,000 paid $14.00 for reserved seats.
26,000 paid $5.00 for general seats.