SOLUTION: in a recent international year 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 integ

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: in a recent international year 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 integ      Log On


   

Question 1130257: in a recent international year 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 51 and the U.S. won more then china who won more than Romania how many medals did each team win?
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
If the sum of three consecutive integer is 51,


    (n-1) + n + (n+1) = 51,


then


     3n = 51,   n  = 51/3 = 17,


which means that the middle number of the three is 17, one third of the given sum.


Hence, Romania won 16 medals, China won 17 medals and U.S. won 18 medals.    ANSWER


The lesson to learn from the solution is THIS : 

    If you are given the sum of three consecutive integer numbers, then the middle number is one third of the sum,

    and you can quickly calculate it mentally without writing any equation/equations.