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Algebra/Algebra II/ Trig Honors word problem


Varun has five rings, each weighing 18 g, made of an alloy of 10% silver and 90% gold. He decides to melt down the rings and add enough silver to reduce the gold content to 75%%. How much silver should he add?

The answer is 18 g of silver but I'm not sure how to get to that answer.

Total amount of gold in all 5 rings = 90/100 * 18 * 5 =81 g

Total amount of silver in all 5 rings = 10/100 * 18 * 5 =9 g

Let the required amount of silver to be added to dilute the gold content to 75% be x g.

Then 81/(x + 18*5)= 75/100    (Note: x+18*5 denotes the new overall total amount of alloy)

81/(x + 90 )= 75/100

x+ 90 =108

Therefore, x = 18 g (shown)

Hope this helps. Peace.


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Frederick Koh


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