Question 1121352
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Here is a completely different way of solving mixture problems like this, where two "ingredients" are being mixed.<br>
I find this method much easier and faster than the traditional algebraic method.<br>
(1) Find where the percentage of the mixture (the final alloy, 75%) lies between the percentage of the original ingredient (55%) and the percentage of the ingredient being added (pure silver, 100%):
100-55 = 45
75-55 = 20
20/45 = 4/9<br>
(2) The percentage of the final alloy is 4/9 of the way from 55% to 100%.<br>
That means 4/9 of the mixture must be the ingredient that is being added.<br>
So let 4x be the amount of the ingredient being added and 9x be the amount of the final alloy; that makes 5x the amount of the original alloy.<br>
Since the amount of the original alloy was 100g, 5x=100g  -->  x=20g.  So the amount of pure silver that needs to be added is 4x = 80g.<br>
And the amount of the final alloy is 5x+4x = 9x = 180g.