document.write( "Question 116992This question is from textbook
\n" ); document.write( ": Thanks for your help on this one: On an 18-hole golf course, there are par-3 holes, par-4 holes and par-5 holes. A golfer who shoots par on every hole has a score of 72. The sum of the number of par-3 and the number of par-5 holes is 8. How many of each type of hole are there on the golf course? \n" ); document.write( "
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On an 18-hole golf course, there are par-3 holes, par-4 holes and par-5 holes. A golfer who shoots par on every hole has a score of 72. The sum of the number of par-3 and the number of par-5 holes is 8. How many of each type of hole are there on the golf course?
\n" ); document.write( "Let:
\n" ); document.write( "x = no. of par 3 holes
\n" ); document.write( "y = no. of par 4 holes
\n" ); document.write( "z = no. of par 5 holes:
\n" ); document.write( ":
\n" ); document.write( "We know:
\n" ); document.write( "x + y + z = 18
\n" ); document.write( ":
\n" ); document.write( "3x + 4y + 5z = 72
\n" ); document.write( ":
\n" ); document.write( "It says,\"The sum of the number of par-3 and the number of par-5 holes is 8.\"
\n" ); document.write( "x + z = 8
\n" ); document.write( "or
\n" ); document.write( "z = (8-x)
\n" ); document.write( ":
\n" ); document.write( "In the 1st equation substitute (8-x) for z:
\n" ); document.write( "x + y + (8-x) = 18
\n" ); document.write( "x - x + y = 18 - 8
\n" ); document.write( "y = 10 par 4 holes
\n" ); document.write( ":
\n" ); document.write( "In the 2nd equation substitute 10 for y and (8-x) for z
\n" ); document.write( "3x + 4(10) + 5(8-x) = 72
\n" ); document.write( "3x + 40 + 40 - 5x = 72
\n" ); document.write( "3x - 5x + 80 = 72
\n" ); document.write( "-2x = 72 - 80
\n" ); document.write( "-2x = -8
\n" ); document.write( "x = -8/-2
\n" ); document.write( "x = 4 par 3 holes
\n" ); document.write( "Then
\n" ); document.write( "8 - 4 = 4 par 5 holes
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check 4(3) + 10(4) + 4(5) =
\n" ); document.write( "12 + 40 + 20 = 72
\n" ); document.write( ":
\n" ); document.write( " \n" ); document.write( "
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