Mixture word problem?

Question

A jeweler has 5 rings, each weighting 18g, made of an alloy of 10% silver and 90% gold. He melts down the rings and wants to add enough silver to reduce the gold content to 75%. How much silver should he add.

The answer is 18 grams of silver i just need to figure out the equation how to get that answer.

thanks for your answers...I already figured it out 9+x=.25(90+x)

Answer 1

After melting down the rings, he has a total weight of 5*18 = 90 g. This will consist of 0.1*90 = 9 g silver, 81 g gold.

To make the gold 75%, we need a total of 81/0.75 = 108 g of metal. We need to add 108 - 90 = 18 g silver

Answer 2

Since he wants 75% of the resulting alloy to be gold, he wants 25% of it to be silver. So the total amount of silver in the rings, plus the amount of pure silver he adds, will equal 25% of the final alloy.

The jeweler has 5 rings, so the total amount of weight is 5*18 = 90g. 10% of this is silver, which is 9 g.

Let "S" be the number of grams of pure silver to add.
After he adds S grams of silver, he gets 90+S grams of metal. 25% of this is 0.25(90+S). So the equation we have is:
9 + S = 0.25(90+S)

Answer 3

If gold is reduced to 75% of the mixture, then silver is 25% of the mixture.

original amount of silver + amount of pure silver = 25% of the total amount of the mixture

0.10(5)(18) + x = 0.25(0.9(5)(18) + 0.10(5)(18) + x)

9 + x = 0.25(90 + x)
9 + x = 22.5 + 0.25x
x - 0.25x = 22.5 - 9
0.75x = 13.5
x = 18

Answer: 18 grams of silver

Answer 4

add the masses together for the 'melting'
mass = 5 x 18g = 90g
90% gold means 90g x 90% = 81g of gold
in order to be 75% gold the final mass (not 90g) must be enough that the 81g of gold is 75%
mass = 81/75% = 108g
the difference between the initial amount of silver (90g x 10% = 9g) and the final amount (108g x %25 = 27g) is that needs to be added

Answer 5

Wt = 5*18 = 90 g
Wt gold = .9*Wt = 81 g
.75 Wn = 81
Wn = 81/.75 = 108
Was (Weight added silver) = Wn-Wt = 108-90 = 18 g