Question 4
At the end of the season, the total prize money in a football tipping competition is shared among the five place-getters under these rules:
(i) All prizes are different positive whole numbers of dollars.
(ii) First prize is the sum of second and third prizes.
(iii) Second prize is the sum of fourth and fifth prizes.
(iv) The higher the placing, the larger the prize. There are no ties.
(1) Find the smallest possible total prize money. (3 points)
(2) If the total prize money is 72 dollars, find all possible distributions among the five place-getters. (5 points)
(i) All prizes are different positive whole numbers of dollars.
(ii) First prize is the sum of second and third prizes.
(iii) Second prize is the sum of fourth and fifth prizes.
(iv) The higher the placing, the larger the prize. There are no ties.
(1) Find the smallest possible total prize money. (3 points)
(2) If the total prize money is 72 dollars, find all possible distributions among the five place-getters. (5 points)