Final answer:
Using arithmetic operations based on the relationships given between the players' scores, we determine that Samson has 15 points, Ruth has 40 points, Delilah has 10 points, and Tim has 5 points.
Step-by-step explanation:
The problem presents a mathematics challenge where we need to determine the number of points each player has after a board game. Using the given information, we can set up equations and solve them step by step.
Let's begin with what we know: Samson ended the game with 15 points.
Ruth had five points less than three times Samson's points, which can be represented as Ruth's points = 3 × Samson's points - 5. If we substitute Samson's points with 15, we get Ruth's points = 3 × 15 - 5 = 45 - 5 = 40.
Twice the number of Delilah’s points is 20 less than Ruth's points, which can be formulated as: 2 × Delilah's points = Ruth's points - 20. Plugging in Ruth's points we get 2 × Delilah's points = 40 - 20 = 20, hence Delilah's points = 20 / 2 = 10.
Tim has ⅓ the number of Samson’s points. Since Samson has 15 points, Tim's points = 15 ÷ 3 = 5.
In conclusion, the final point tallies for each player are: Samson has 15 points, Ruth has 40 points, Delilah has 10 points, and Tim has 5 points.