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.