document.write( "Question 103103: The admission fee at a small fair is $1.50 for children and $4.00 for
\n" ); document.write( "adults. On a certain day, 2200 people enter the fair and $5050 is
\n" ); document.write( "collected. How many children and how many adults attended? \n" ); document.write( "
Algebra.Com's Answer #74962 by doukungfoo(195)\"\" \"About 
You can put this solution on YOUR website!
Ok first set some variables.
\n" ); document.write( "Lets call adults x
\n" ); document.write( "Lets call children y
\n" ); document.write( "Given: 2200 people attend the fair
\n" ); document.write( "using x and y write and equation to express this
\n" ); document.write( "x + y = 2200
\n" ); document.write( "Now lets look at what else we are told
\n" ); document.write( "Given: Child admission fee is $1.50
\n" ); document.write( "Adult admission fee is $4.00
\n" ); document.write( "The total amount collected is $5050.00
\n" ); document.write( "Now again using x and y write and equation to express this known information
\n" ); document.write( "4x + 1.5y = 5050
\n" ); document.write( "In other words $4 times the number of adults (x) plus $1.50 times the number of children (y) equals $5050
\n" ); document.write( "Ok so now we have a system of equations that we can use to solve for x and y
\n" ); document.write( "x + y = 2200
\n" ); document.write( "AND
\n" ); document.write( "4x + 1.5y = 5050
\n" ); document.write( "To solve the equations I will demonstrate the substitution method.
\n" ); document.write( "Take the first equation and set it equal to x
\n" ); document.write( "x + y = 2200
\n" ); document.write( "subtract y from both sides
\n" ); document.write( "x + y - y = 2200 - y
\n" ); document.write( "x = 2200 - y
\n" ); document.write( "Now since we have shown that x equals 2200-y we can substitute that for x in the second equation and solve for y
\n" ); document.write( "4x + 1.5y = 5050
\n" ); document.write( "4(2200-y) + 1.5y = 5050
\n" ); document.write( "multiply 4 across (2200-y)
\n" ); document.write( "8800 - 4y + 1.5y = 5050
\n" ); document.write( "combine like terms
\n" ); document.write( "8800 - 2.5y = 5050
\n" ); document.write( "subtract 8800 from both sides
\n" ); document.write( "8800 - 8800 - 2.5y = 5050 - 8800
\n" ); document.write( "-2.5y = -3750
\n" ); document.write( "divide both sides by -2.5
\n" ); document.write( "-2.5y/-2.5 = -3750/-2.5
\n" ); document.write( "y = 1500
\n" ); document.write( "Answer: 1500 children attended the fair
\n" ); document.write( "Now use this answer to find x
\n" ); document.write( "Take the first equation and substitute y with 1500
\n" ); document.write( "x + y = 2200
\n" ); document.write( "x + 1500 = 2200
\n" ); document.write( "subtract 1500 from both sides
\n" ); document.write( "x + 1500 - 1500 = 2200 - 1500
\n" ); document.write( "x = 700
\n" ); document.write( "Answer: 700 adults attended the fair
\n" ); document.write( "Check both answers in both equations
\n" ); document.write( "first equation:
\n" ); document.write( "x + y = 2200
\n" ); document.write( "700 + 1500 = 2200
\n" ); document.write( "2200 = 2200
\n" ); document.write( "Now the second equation:
\n" ); document.write( "4x + 1.5y = 5050
\n" ); document.write( "4(700) + 1.5(1500) = 5050
\n" ); document.write( "2800 + 2250 = 5050
\n" ); document.write( "5050 = 5050\r
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