document.write( "Question 1124210: A stadium has 54000 seats. Seats sell for ​$30 in Section​ A, ​$24 in Section​ B, and ​$18 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium takes in ​$1382400 from each​ sold-out event. How many seats does each section​ hold? \n" ); document.write( "
Algebra.Com's Answer #753279 by VFBundy(438)\"\" \"About 
You can put this solution on YOUR website!
\"The number of seats in Section A equals the total number of seats in Sections B and C.\"
\n" ); document.write( "
\n" ); document.write( "This tells us that the number of seats in Section A is exactly half of the 54,000 seats the stadium holds...27,000 seats...with the other two sections combining for the remaining 27,000 seats. Therefore, with regard to the number of seats in Sections B and C, we know:
\n" ); document.write( "
\n" ); document.write( "B + C = 27000
\n" ); document.write( "
\n" ); document.write( "\"Seats sell for ​$30 in Section​ A, ​$24 in Section​ B, and ​$18 in Section C.\"
\n" ); document.write( "\"Suppose the stadium takes in ​$1,382,400 from each​ sold-out event.\"
\n" ); document.write( "
\n" ); document.write( "We already know that there are 27,000 seats in Section A that sell for $30. We also know how much the seats in the other sections sell for, as well as the total \"take\" from a sell-out. But, we still do not know how many seats are in Section B and Section C. Therefore, with regard to the money, we know:
\n" ); document.write( "
\n" ); document.write( "30(27000) + 24B + 18C = 1382400
\n" ); document.write( "
\n" ); document.write( "Simplify this:
\n" ); document.write( "810000 + 24B + 18C = 1382400
\n" ); document.write( "
\n" ); document.write( "24B + 18C = 572400
\n" ); document.write( "
\n" ); document.write( "We are left with two equations:
\n" ); document.write( "
\n" ); document.write( "B + C = 27000
\n" ); document.write( "24B + 18C = 572400
\n" ); document.write( "
\n" ); document.write( "Multiply the first equation by -18:
\n" ); document.write( "
\n" ); document.write( "-18B - 18C = -486000
\n" ); document.write( "24B + 18C = 572400
\n" ); document.write( "
\n" ); document.write( "Add the two equations together:
\n" ); document.write( "6B = 86400
\n" ); document.write( "
\n" ); document.write( "Solve for B:
\n" ); document.write( "B = 14400
\n" ); document.write( "
\n" ); document.write( "This means there are 14,400 seats in Section B.
\n" ); document.write( "
\n" ); document.write( "Looking at the equation B + C = 27000, if you plug in 14400 for B, this would mean C = 12600. So, Section C has 12,600 seats.
\n" ); document.write( "
\n" ); document.write( "In summary:
\n" ); document.write( "Section A = 27,000 seats
\n" ); document.write( "Section B = 14,400 seats
\n" ); document.write( "Section C = 12,600 seats
\n" ); document.write( "
\n" ); document.write( "-------------------------------------------------
\n" ); document.write( "
\n" ); document.write( "Double-check:
\n" ); document.write( "
\n" ); document.write( "Section A: 27,000 seats @ $30 each = $810,000
\n" ); document.write( "Section B: 14,400 seats @ $24 each = $345,600
\n" ); document.write( "Section C: 12,600 seats @ $18 each = $226,800
\n" ); document.write( "
\n" ); document.write( "$810,000 + $345,600 + $226,800 = $1,382,400 \n" ); document.write( "
\n" );