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A concert sold general admission tickets for 
$47.50 and lowerlevel 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
290 seats for general admission and 705 seats for lower level
565 seats for general admission and 430 seats for lower level
515 seats for general admission and 480 seats for lower level

A concert sold general admission tickets for $47.50\$47.50 and lowerlevel seating for $97.50\$97.50. The 995995 tickets sold took in $68,762.50\$68,762.50 How many seats were sold for general admission and how man seats were sold for lower-level seating?\newline470470 seats for general admission and 525525 seats for lower level\newline290290 seats for general admission and 705705 seats for lower level\newline565565 seats for general admission and 430430 seats for lower level\newline515515 seats for general admission and 480480 seats for lower level

Full solution

Q. A concert sold general admission tickets for $47.50\$47.50 and lowerlevel seating for $97.50\$97.50. The 995995 tickets sold took in $68,762.50\$68,762.50 How many seats were sold for general admission and how man seats were sold for lower-level seating?\newline470470 seats for general admission and 525525 seats for lower level\newline290290 seats for general admission and 705705 seats for lower level\newline565565 seats for general admission and 430430 seats for lower level\newline515515 seats for general admission and 480480 seats for lower level
  1. Define variables: Let's define variables: Let x x be the number of general admission tickets and y y be the number of lower-level seating tickets.
  2. Write equations: Write the equations based on the total number of tickets and the total revenue. Equation 11: x+y=995 x + y = 995 (total tickets). Equation 22: 47.50x+97.50y=68762.50 47.50x + 97.50y = 68762.50 (total revenue).
  3. Solve first equation: Solve the first equation for x x : x=995y x = 995 - y .
  4. Substitute and simplify: Substitute x x in the second equation: 47.50(995y)+97.50y=68762.50 47.50(995 - y) + 97.50y = 68762.50 .
  5. Solve for y: Simplify and solve for y y : 47252.5047.50y+97.50y=68762.50 47252.50 - 47.50y + 97.50y = 68762.50 . Combine like terms: 50y=21510 50y = 21510 . Then, y=430 y = 430 .
  6. Substitute for x: Substitute y=430 y = 430 back into the equation for x x : x=995430 x = 995 - 430 , so x=565 x = 565 .
  7. Check solution: Check the solution by substituting x=565 x = 565 and y=430 y = 430 back into the original revenue equation: 47.50×565+97.50×430=26862.50+41925=68787.50 47.50 \times 565 + 97.50 \times 430 = 26862.50 + 41925 = 68787.50 .

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