document.write( "Question 164624This question is from textbook
\n" ); document.write( ": Ticket sales: A science museum charges $10 for a regular admission ticket, but members recieve a discount of $3 and students are admitted for $5. Last saturday, 750 tickets were sold for a total of $5400. If 20 more student tickets than regular tickets were sold, how many of each type of ticket were sold?\r
\n" ); document.write( "\n" ); document.write( "I need to know the steps in which they used to solve this? \n" ); document.write( "

Algebra.Com's Answer #121310 by MRperkins(300) $\"\"$ $\"About$

You can put this solution on YOUR website!
Ok, the first thing we need to do is set up our formulas.
\n" ); document.write( "Let's use:
\n" ); document.write( "r = regular admission tickets = $10
\n" ); document.write( "m = members admission tickets = $7
\n" ); document.write( "s = student admission tickets = $5
\n" ); document.write( "So we know that 750 tickets were sold so:
\n" ); document.write( " $\"r%2Bm%2Bs=750\"$ \r
\n" ); document.write( "\n" ); document.write( "and\r
\n" ); document.write( "\n" ); document.write( "We know the price of the tickets and the total dollar amount sold was $5400 so:
\n" ); document.write( "Price of each ticket times the number of that ticket sold equals $5400 or:
\n" ); document.write( " $\"%2410r%2B%247m%2B%245s=%245400\"$
\n" ); document.write( "We also know that 20 more student tickets than regular tickets were sold so:
\n" ); document.write( " $\"s=r%2B20\"$ \r
\n" ); document.write( "\n" ); document.write( "Now for the fun part :/)
\n" ); document.write( "Use the elimination method to solve:
\n" ); document.write( "10r+7m+5s=5400
\n" ); document.write( " r+ m+ s=750
\n" ); document.write( "We want to eliminate m because it is the only variable that is not in the s=r+20 equation.
\n" ); document.write( "so:
\n" ); document.write( "Multiply everything in the bottom equation by 7.
\n" ); document.write( " 10r+ 7m+ 5s=5400
\n" ); document.write( "(7)r+(7)m+(7)s=(7)750
\n" ); document.write( "OR
\n" ); document.write( "10r+7m+5s=5400
\n" ); document.write( " 7r+7m+7s=5250
\n" ); document.write( "Now we can subtract and get
\n" ); document.write( " $\"10r-7r%2B7m-7m%2B5s-7s=5400-5250\"$
\n" ); document.write( "combine like terms:
\n" ); document.write( " $\"3r-2s=150\"$
\n" ); document.write( "Now it is time to use the equation: $\"s=r%2B20\"$
\n" ); document.write( "Substitute r+20 for s so:
\n" ); document.write( " $\"3r-2%28r%2B20%29=150\"$
\n" ); document.write( "Distribute
\n" ); document.write( " $\"3r-2r-40=150\"$
\n" ); document.write( "combine like terms
\n" ); document.write( " $\"r-40=150\"$
\n" ); document.write( "add 40 to both sides and get $\"r=190\"$
\n" ); document.write( "now substitute 190 for r in the equation and solve for s: $\"s=%28190%29%2B20\"$
\n" ); document.write( "and you get $\"s=210\"$
\n" ); document.write( "go back to the first equation and plug in 190 for r and 210 for s:
\n" ); document.write( " $\"r%2Bm%2Bs=750\"$
\n" ); document.write( " $\"%28190%29%2Bm%2B%28210%29=750\"$
\n" ); document.write( "Solve for m:
\n" ); document.write( "combine like terms:
\n" ); document.write( " $\"m%2B400=750\"$
\n" ); document.write( "subtract 400 from both sides:
\n" ); document.write( " $\"m=350\"$ \r
\n" ); document.write( "\n" ); document.write( "Elimination and substitution are fun. It gets better as you get used to them. \n" ); document.write( "

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