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Got a commission to redesign a wedding band, melting down the original, add some metal and redesign it, so far so good.
When I get the lens and realize that the original is a 9ct and the new design is to be a 18ct, jumped to me: “Nuno, where are the notes with the formulas for these things?!”.
So, had no idea where they were!

But still, was pretty sure that would find the numbers needed to do it, and it started like this:1

Numbers, numbers, numbers, nothing wrong with this but, none of them were matching!

So focus, aaand think. You have the total weight of the ring, 2.64g, and it’s a 9ct, so 0.99 of fine gold (37.5%, the rest I’ll mark it as rest of alloy, 62.5%). With this very simple rule (we call it three simple rule, still don’t know its name in english, no one seemed to recognize it), we can find one number/value from the other three, being these related in pairs and each one with their own units.

Lets make it simple, it’s called three simple rule for a reason!

An athelet runs 35 km in 3 hours.

How long would he take to run 50 km?

(this is like primary school maths! But I find it very usefull in the jewellery counts of all kind, specially when it comes to alloys)

So, how long?!

3simple

This is how it would be done following this formula. Organize the numbers we have, related vertically, so, 35 with 50, both km, and 3h stands with the X, that is going to be the time he needs to run 50km.

Now we multiply 50 by 3 and divide by 35 to get the missing number X.

50 x 3 % 35 = X                     X = 4,29

It would take him 4h 29m to run the 50km.

Back to business then, I knew the total weight (2.64), the fine gold (0.99) and the rest of the alloy (1.65).

Have more than enough values, because we have as well the percentages, 37.5 of the fine gold in the 9ct original ring, the 62.5% of r.alloy, and the 75% (18ct) that we want to reach of fine gold. That’s probably why I went mad at first!

The right way to do it is here:

2

Start with the alloy value, 1.65g, this value is not going to change, I want to had enough gold to bring it from 9ct (37.5% f. gold, 62.5% r. alloy) to 18ct (75% f. gold, 25%r. alloy), so, just gold needs to be added right?! 1.65 is at the moment 62.5% of the alloy, but will turn into 25%, we’ll write down 1.65 (g) to 25 (%) and the X to 100 (%), multiply 1.65 by 100 and divide by 25 and have 6.6 (g), which corresponds to 100% of the 18ct final alloy. 6.6g minus 1.65g will be 4.95 (of fine gold), we already have 0.99g of fine gold in the alloy so, take that back 4.95 – 0.99 =3.96. This is the amount of fine gold that I need to add and voila!

The same formula is used to confirm the numbers all match.3

And it’s time for the fun stuff!

4

5

Hope this helps you in future commissions as well, it saves the hassle and some money that might be lost in scrapping, this case is the hassle and the intention of the commission to keep the original inside the new design, the attachment of old and new material and all that comes with it.

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