How do you reduce a 90% gold content into 75%

[acen_gr]

The title says it all.

Say you have 5 rings, each weighing 18 grams (10% alloy and 90% gold).
If you would melt them all and add silver to make it 75% gold,

1) how much silver do you have to add?

2) Does melting 5 rings with 18grams each give 90 grams in total?

3) is this equation to solve for this problem right?

let x = amount of silver to add
total grams = 90 g

total grams (.90) + x silver (100%) = total grams + x (.75)
90(.9) + 1x = 90(.75)
81 + x = 67.5 + .75x
x = -54

4) Am I doing/thinking them all wrong?

thanks.

 

[Borek]

This is a homework type question, I am moving it to HW forum.

You are right about total mass of gold being 90 g, but this equation

total grams (.90) + x silver (100%) = total grams + x (.75)

is wrong (and to be honest I am not even able to decipher what you tried to do).

Let's assume (like you nicely did), that you added x g of silver.

If so, what is the formula for the total mass of the alloy?

What is the formula for the percentage of gold in this alloy?

 

[member 392791]

more importantly, why do you want to turn more gold to less? That stuff is more expensive than silver anyway

 

[JohnRC]

more importantly, why do you want to turn more gold to less? That stuff is more expensive than silver anyway

He is not wanting to turn more into less; he is wanting to turn more into even more.

Starting with x gram of gold and y gram of other stuff to make (x + y) gram of "gold" (90%), he wants to add z gram of other stuff to make (x + y + z) gram of "gold" (75%).

And no, even if it is not a homework question, he is not likely to be pulling a swindle. 75% gold is 18 carat gold, which is a much more useful material for certain purposes than pure gold.

 

[LudusRex]

I would approach this problem using the principles of conservation of mass and stoichiometry. The first step would be to calculate the amount of gold present in the 5 rings:

Gold content = 5 rings x 18 grams/ring x 0.90 (90% gold) = 81 grams

Next, we need to determine the amount of silver that needs to be added to reduce the gold content from 90% to 75%. This can be done by setting up a proportion:

(81 grams gold / total grams) = (75% / 100%)

Solving for total grams, we get:

Total grams = 81 grams gold / 0.75 = 108 grams

Since we started with 90 grams of gold, we need to add 18 grams of silver (108 grams - 90 grams = 18 grams) to achieve a 75% gold content.

To answer your specific questions:

1) We need to add 18 grams of silver to reduce the gold content from 90% to 75%.

2) Yes, melting 5 rings with 18 grams each would give a total of 90 grams.

3) Your equation is correct, but the value for x is incorrect. It should be 18 grams, not -54 grams.

4) You are on the right track, but it is important to use the correct values and units in your calculations. It is also helpful to clearly define your variables and show all steps in your calculations.

I hope this helps!