Problema 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 highest point total. What is the smallest total score that Beth can have?
Answer provided by our tutors
The total of the three scores will be:
3*(5 + 3 + 1) = 27
The average score is:
27/3 = 9
The highest point total is and odd number not less than 9.
If the highest point is 9 this means that Beth had the following scores:
Beth: 3, 3, 3
Amanda:1, 5, 1
Sarah: 5, 1, 5
but then Sarah will have 11 points and this contradicts with assumption that Beth has the highest point total.
The next possible highest point total is 11, that is:
Beth: 5, 5, 1
Amanda: 3, 1, 5
Sarah: 1, 3, 3
The smallest total score that Beth can have is 11.