How do I set up this Linear Equation word problem??

E

eusazwi

New member
Joined
Nov 30, 2007
Messages
6
Any help would be greatly appreciated:

The directions are solve by using a system of equations.

A goldsmith has two gold alloys. The first alloy is 40% gold; the second alloy is 60% gold. How many grams of each should be mixed to produce 20 grams of an alloy that is 52% gold?

The final answer is:
8 grams of 40% gold, 12 grams of 60% gold.


My attempt:
40x + 60y = 20 :?:

(but that doesn't give me 2 equations in which I thougt I would next us the elimination method to find x and y)
 
You don't have to use two equations. You can use one.

\(\displaystyle 0.40x+0.60(20-x)=0.52(20)\)

But, if you must:

\(\displaystyle x+y=20\)

\(\displaystyle 0.40x+0.60y=10.4\)
 
What's Rule #1, eusazwi? I will tell you. Rule #1 is Name Stuff. Write down your definitions. Look at them on the page. They will speak to you.

Watch...

F = gm of 40% Gold Alloy
S = gm of 60% Gold Alloy

Now they begin to speak.

"How many grams of each should be mixed to produce 20 grams"

Oh, then F + S = 20 gm <== Here, we are equating grams of alloy.

"alloy that is 52% gold"

F*0.40 + S*0.60 = (20 gm)*0.52 <== Here, we are equating grams of Gold.

Notice that your one equation is very confused. WRITING DOWN the definitions and looking at them will fix this.

Let's see what you get.
 
:D :D :lol: :shock: 8-) This site Rulessss.........

Thanks Galactus and Tkhunny, that info got me far enough to understand what was going on in order for me to complete the problem. I'm so happy I found this Forum.

Later,
Dean
 
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