A golden brick of 0.950 purity weighs 6300 grams. What amount of pure

Hi VeritasKarishma
I tried to solve above problem using weighted average formula but the answer I got is not even in the option and off by 2600gms (approx).
Then I solved it using concentration formula since the amount of gold remains the same and its only the volume/weight of the final product that is changing. Then I got the correct answer.

Could we even solve this problem using weighted average? If yes, how? Please help. I am trying to get my head around weighted average and every now and then I get stuck in such a problem.

Here is how I substituted values in both the formulae :
1: weighted average

W(g)/W(c) = (A(copper) - A(avg)/A(gold)-A(avg))
5985/w(c) = (1-0.9)/(0.95-0.9) Note: brick is 95% gold so W(g) = 6300 * 0.95 = 5985gms
W(c) = 2995.5 gms obviously incorrect!!

2: Concentration way

ViCi = VfCf
(0.95)6300 = Vf(0.9)
Vf = 6650

amount of copper used = 6650 - 6300 = 350gms correct.

Edit 1:

Hi VeritasKarishma

I found my mistake. I should have considered ratio of mixtures instead of ratio of two components. duh!!

0%|------------------90%----|95%
(100%Copper) (Desired) (given 95% pure gold bar = 6300gms)

w1/w2 = 5/90 = 1/18
since w2 is 6300 gms

w1 = (1/18) * 6300 = 350gms!!

Hi Rogermoris
I think you meant
ViCi = VfCf
(0.95)6300 = Vf(0.9)
Vf = 6650

amount of copper used = 6650 - 6300 = 350gms

Is there a way to solve this problem without multiplying by 0.9 and dividing by 0.95? Seems to take a lot of time calculating -- are there any shortcuts?

Given

• A golden brick of 0.950 purity weighs 6300 grams.

To Find

• The amount of pure copper should be added to lower its purity to 0.900.

Approach and Working Out

• Total weight = 6300 gm.

o Amount of copper = 0.05 of 6300 = 315 gm.
o Gold= 6300 – 315 = 5985 gm
• 5985 gm gold must be 0.9 portion in the new brick.

o Total amount = \(\frac{5985}{0.9}\) = 6650 gm.
o Copper to be added = 6650 – 6300 = 350 gm

Correct Answer: Option D

It can simply be considered as mixing two solutions together, one with 95% gold and another with 0% gold (pure copper) to give 90% gold.

\(\frac{wCopper}{wBrick} = \frac{(95 - 90)}{(90 -0 )} = \frac{1}{18}\)

Hence for every 18 parts of brick, 1 part of copper should be added.

Weight of copper to be added \(= \frac{6300}{18} gm = 350 gms\)

Answer (D)