SOLUTION: 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 hig

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: 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 hig      Log On

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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?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The total of the three scores must be 3%285%2B3%2B1%29=3%2A9 ,
which makes the average score 3%2A9%2F3=9%7D%7D+.%0D%0ASo+the+highest+scorer+must+score+more+than+%7B%7B%7B9 .
The highest score must also be odd, because it is the sum of three odd numbers.
Could it be 11 ?

There are 10 possible scores:
1%2B1%2B1=3
1%2B1%2B3=5
1%2B1%2B5=7
1%2B3%2B3=7
1%2B3%2B5=9
1%2B5%2B5=11
3%2B3%2B3=9
3%2B3%2B5=11
3%2B5%2B5=13
5%2B5%2B5=15
If Beth scores were 1, 5, and 5 (in any order),
the remaining scores would be 1, 1, 3, 3, 3, and 5.
There is at least one way in which Amanda and Sarah could have earned those scores,
and still have lower total score:
, so Beth could have a score of 11, and still be the highest scorer.
The smallest total score that Beth can have is highlight%2811%29 .