SRL Archive - Mathematics

Joe has a ring weighing 10 grams made of an alloy of 14% silver and the rest gold. He decides to melt down the rings and add enough silver to reduce the gold content to 72%. How many grams of silver should he add?

I'm trying:

(1.4 + x)/8.6=28/72

x=1.944444?

And how would I put the answer in 2 significant figures? Do the numbers before the decimal count? And when do they not count?

Thanks.

P.S I never took Calculus or Physics in High School and I'm now I'm taking them both in college. :{

Joe has a ring weighing 10 grams made of an alloy of 14% silver and the rest gold. He decides to melt down the rings and add enough silver to reduce the gold content to 72%. How many grams of silver should he add?

Grams_of_Gold / (Initial Weight[g] + Grams_of_Silver_Needed_to_Reduce_Gold_Percentage[x g]) = Desired_Percentage_of_Gold

8.6 / (10 + x) = 0.72 (72%)
x = 1.94^_g
or
x = 35/18g
or
x = 1 17/18g

That's how I solved it. o.o

What is the purity of the silver and gold? If you are assuming 100% purity of substances:

find how many grams per %…
1.4g Ag + 8.6g Au = 10g ring

find how much silver to add to make 72% gold. Keep the total at ratio at 100
(1.4g + x)Ag / (8.6g)Au = 28 Ag / 72 Au

Solve for x
x = 1.94444

**************
same as what you did… both ways get the same answer…
and two sig figs would be 1.9 - here is a good teach http://www.sciencebyjones.com/sig_figs.htm

small recap on sig figs:
sig figs when adding/subtracting:
there must be the same amount of places after the decimal points as the lowest number of places. so, 8.92 + 9.1 + 8.666 = 26.7
sig figs when multiplying/dividing:
the number of sig figs must be the same as the number with the lowest number of sig figs. so, 6.766 * 3.4456 / 1.2 = 19

With sigfigs and logs/exponentials, you keep the same number of decimal places as you had sig figs in the original question. (Odd eh?)