SOLUTION: At the Winter Olympics in Lillehammer, Norway, the number of gold medals Canada won was half the number of silver medals. Canada won 3 silver medals for every 2 bronze medals it wo

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: At the Winter Olympics in Lillehammer, Norway, the number of gold medals Canada won was half the number of silver medals. Canada won 3 silver medals for every 2 bronze medals it wo      Log On


   

Question 1203159: At the Winter Olympics in Lillehammer, Norway, the number of gold medals Canada won was half the number of silver medals. Canada won 3 silver medals for every 2 bronze medals it won. The total number of gold and bronze medals was one more than the number of silver medals.
How many medals of each type did Canada win?
Answer by ikleyn(52800) About Me  (Show Source):
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At the Winter Olympics in Lillehammer, Norway, the number of gold medals Canada won
was half the number of silver medals.
Canada won 3 silver medals for every 2 bronze medals it won.
The total number of gold and bronze medals was one more than the number of silver medals.
How many medals of each type did Canada win?
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x = # of gold medals;

2x = # of silver medals;

silver%2Fbronze = 3%2F2, which means bronze = %282%2Asilver%29%2F3 = %282%2A%282x%29%29%2F3 = %284x%29%2F3.


    gold + bronze = silver + 1,

or

    x + %284x%29%2F3 = 2x + 1.


Simplify and find x.  First multiply both sides by 3

    3x + 4x = 6x + 3

    7x = 6x + 3

    7x - 6x = 3

       x    = 3.


ANSWER.  3 gold medals; 2*3 = 6 silver medals;  %284%2A3%29%2F3 = 4 bronze medals.

Solved.