Problema Solution
In a recent International Gymnastics competition, the U.S., China, and Romania were the big winners. if the total number of medals won by each team are three consecutive integers whose sum is 36 and the U.S. won more then China who won more then Romania, how many medals did each team win?
Answer provided by our tutors
Since the amount of medals won by each country is represented by 3 consecutive integers, and since Romania won the least amount of medals, let the amount of medals Romania won be R. This will be the smallest number of the 3 numbers.
Therefore, the next consecutive integer, R + 1 would represent the amount of medals China won, and R + 2 would represent the amount of medals the USA won
Since the 3 won a total of 33 medals, it follows that:
R + R + 1 + R + 2 = 33
3R + 3 = 33
3R = 30
Therefore,
Romania won R, or medals, while
China won (10 + 1) medals, and
the USA won (10 + 2) medals.