document.write( "Question 1014123: Amanda, Beth, and Sarah run three races. in each race, one of them earns 5 points, one of them earns 3 points, and one of them earns 1 point. After the three races Beth has the highest point total. What is the smallest total score that Beth can have? \n" ); document.write( "

Algebra.Com's Answer #630484 by KMST(5328) $\"\"$ $\"About$

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The total of the three scores must be $\"3%285%2B3%2B1%29=3%2A9\"$ ,
\n" ); document.write( "which makes the average score $\"3%2A9%2F3=9%7D%7D+.%0D%0ASo+the+highest+scorer+must+score+more+than+%7B%7B%7B9\"$ .
\n" ); document.write( "The highest score must also be odd, because it is the sum of three odd numbers.
\n" ); document.write( "Could it be $\"11\"$ ?
\n" ); document.write( "
\n" ); document.write( "There are 10 possible scores:
\n" ); document.write( " $\"1%2B1%2B1=3\"$
\n" ); document.write( " $\"1%2B1%2B3=5\"$
\n" ); document.write( " $\"1%2B1%2B5=7\"$
\n" ); document.write( " $\"1%2B3%2B3=7\"$
\n" ); document.write( " $\"1%2B3%2B5=9\"$
\n" ); document.write( " $\"1%2B5%2B5=11\"$
\n" ); document.write( " $\"3%2B3%2B3=9\"$
\n" ); document.write( " $\"3%2B3%2B5=11\"$
\n" ); document.write( " $\"3%2B5%2B5=13\"$
\n" ); document.write( " $\"5%2B5%2B5=15\"$
\n" ); document.write( "If Beth scores were 1, 5, and 5 (in any order),
\n" ); document.write( "the remaining scores would be 1, 1, 3, 3, 3, and 5.
\n" ); document.write( "There is at least one way in which Amanda and Sarah could have earned those scores,
\n" ); document.write( "and still have lower total score:
\n" ); document.write( "

, so Beth could have a score of 11, and still be the highest scorer.
\n" ); document.write( "The smallest total score that Beth can have is $\"highlight%2811%29\"$ .
\n" ); document.write( " \n" ); document.write( "

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