Question 663902
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At the 2006 Winter Olympics in Italy, the top medal winner was Germany, which won a total of 29 medals. 
Germany won 1 more silver medal than gold and 5 more gold medals than bronze. 
Find the number of each type of medal won. How do I solve this?
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        Tutor @Theo provided long wordy solution with a lot of unnecessary complications.

        I will give here much shorter solution, which I hope is more clear, more accessible and more instructive.



<pre>
Let x be the number of gold medals Germany won.

Then the number of silver medals is (x+1), according to the problem,

and the number of bronze medals was ((x-5).


Write an equation expressing the total number of medals

    x + (x+1) + (x-5) = 29   (29 in the right side is the given total).


Simplify collecting and combining like terms

    3x - 4 = 29,

    3x = 29 + 4,

    3x = 33,

     x = 33/3 = 11.


So, the number of gold medals was 11;  the number of silver medals was 11+1 = 121;  the number of bronze medals was 11-5 = 6.


<U>CHECK</U>.  The total is  11 + 12 + 6 = 29.   ! correct !
</pre>

At this point, the problem is solved completely.