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 man seats were sold for lower-level seating?470 seats for general admission and 525 seats for lower level290 seats for general admission and 705 seats for lower level565 seats for general admission and 430 seats for lower level515 seats for general admission and 480 seats for lower level
Q. 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 man seats were sold for lower-level seating?470 seats for general admission and 525 seats for lower level290 seats for general admission and 705 seats for lower level565 seats for general admission and 430 seats for lower level515 seats for general admission and 480 seats for lower level
Define variables: Let's define variables: Let x be the number of general admission tickets and y be the number of lower-level seating tickets.
Write equations: Write the equations based on the total number of tickets and the total revenue. Equation 1: x+y=995 (total tickets). Equation 2: 47.50x+97.50y=68762.50 (total revenue).
Solve first equation: Solve the first equation for x: x=995−y.
Substitute and simplify: Substitute x in the second equation: 47.50(995−y)+97.50y=68762.50.
Solve for y: Simplify and solve for y: 47252.50−47.50y+97.50y=68762.50. Combine like terms: 50y=21510. Then, y=430.
Substitute for x: Substitute y=430 back into the equation for x: x=995−430, so x=565.
Check solution: Check the solution by substituting x=565 and y=430 back into the original revenue equation: 47.50×565+97.50×430=26862.50+41925=68787.50.
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