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 w

Question 212874: 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 33 and the U.S. won more than China who won more than Romania, how many medals did each team win?
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
If I understand, the problem is asking:
"What 3 consecutive integers add up to ?
I'll use trial and error
10 + 11 + 12 = 33}}
Bingo- hit it on 1st try
Us won 12
China won 11
Romania won 10

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
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 33 and the U.S. won more than China who won more than Romania, how many medals did each team win?

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.

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