Can you please help me? I am trying to figure out how to solve this problem for hours now:

"A woman need to mix alloy with 16% of silver and an alloy with 28% of silver to obtain 32 ounces of a new alloy with 25% gold. how many ounces of each of the original alloys must she use?

Question

Can you please help me? I am trying to figure out how to solve this problem for hours now:

"A woman need to mix alloy with 16% of silver and an alloy with 28% of silver to obtain 32 ounces of a new alloy with 25% gold. how many ounces of each of the original alloys must she use?

anonymous · Answer

No amount of mixing silver will give you an alloy of 25% gold.

zarkon · Answer

That's too bad since Gold prices are so high now.  oh well. :(

anonymous · Answer

In case you meant "25% silver",$$\frac{16}{100}x+\frac{28}{100}y = 32\frac{25}{100}$$where x is the mass of the first alloy and y the mass of the second alloy. Because the final mass is 32, we also have$$x + y = 32.$$Simplifying the first equation,$$\frac{4x + 7y}{25}=8 \Rightarrow 4x+7y = 200 \Rightarrow 3y = 72 \Rightarrow y = 24 \Rightarrow x = 8.$$

anonymous · Answer

why are x and y represented by different variables? shouldn't they be the same since they are both silver?

anonymous · Answer

I see. it makes sense now. i did not include the variables.

anonymous · Answer

Thank you Krebante

anonymous · Answer

oh, i see what my mistake was. clearly i have math dyslexia

anonymous · Answer

@ math_moron, i believe that different variables are used. u can look at it like two different containers were used.

anonymous · Answer

yeah i read it as mixing an alloy w/ another and then mixing those two with two more that had already been mixed. ><'