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

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
Mentor
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

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.