Question

A concert sold general admission tickets for $47.50 and lower-level seating for $97.50. The 995 tickets sold took in $68,762.50. How many seats were sold for general admission and how many seats were sold for lower-level seating?
470 seats for general admission and 525 seats for lower level

515 seats for general admission and 480 seats for lower level

290 seats for general admission and 705 seats for lower level

565 seats for general admission and 430 seats for lower level

Answer 1

Answer: 565 general admission and 430 lower-level seating tickets sold (Answer (D))

Steps:

Let x be the number of general admission tickets, and y be the number of lower level tickets.

Set up the two equations:

68762.5 = x * 47.50 + y * 97.50       (total price as a sum of individual volumes)

x + y = 995    (sum of individual count = total count of tickets sold)

solve for x, y:

x = 995 - y

plug into the first equation:

68762.5 = (995-y) * 47.50 + y * 97.50

solve for y:

y = 430

then x = 565

x = 565 and y = 430

Answer 2

Answer: 565 General Admission and 430 Lower Level

Step-by-step explanation:

G = General Admission L=Lower Level

47.5G+97.5L=68762.5 <-- This is the equation used to find g and l

G+L=995 <-- This is the equation to prove that g and l for the above equation is true

G=995-L <-- This is used to plug into G in the first equation to find L

47.5(995-L)+97.5L=68762.5 <-- Use Distributive Property

47262.5-47.5L+97.5L=68762.5 <-- Use Associative Property

47262.5+50L=68762.5 <-- Use Subtraction Property of Inequality

50L=21500 <-- Divide by 50 on both sides

L=430 <-- Plug in 430 into G=995-L

G=565 L=430 <-- Plug in both to the first equation to check