Help figuring an equation

PNGento

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Joined
Jan 22, 2019
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3
This is my first post and I wasn't sure which group to post this in, but this one seems the best fit...if there is a better group, please either move this to that group of ask me to delete and then repost in such and such group. Thanks.

This equation was posted on another site, but it is not available to ask questions on that site, so hoping someone here can help me. The equation was posted as an answer to the question "how much 92.5% pure silver and how much pure (100%) silver needs to be mixed to obtain a 94% mixture with a resultant 100g of the 94% alloy. Here is the solution provided:
Beginning of the solution
We now write an equation relating the amounts of pure silver in the two "input" mixtures and in the "output" mixture:
"x" grams at 92.5% silver + (100-x) grams at 100% = 100g at 94%

(x)(0.925) + (100-x)(1.0) = (100)(0.94)
0.925x + 100 - x = 94
6 = 0.075x
6000 = 75x
6000/75 = x
80 = x
End of solution

I understand most of the equation but do not get how the equation was solved to give 6=0.075x. The rest I can do. Can someone help me get from the second line to the third line...all the rest makes sense. (I think it is the 2 x's that is throwing me).

TIA

 

tkhunny

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Apr 12, 2005
Messages
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0.925x + 100 - x = 94




6 = 0.075x
01) 0.925x + 100 - x = 94
02) 0.925x - x + 100 = 94 -- Commutative
03) (0.925x - x) + 100 = 94 -- Associative
04) (0.925 - 1)*x + 100 = 94 -- Distributive
05) -0.075x+ 100 = 94 -- Addition
06) -0.075x + 100 - 100 = 94 - 100 -- Property of Equals (Is there a formal name for "Do the same thing to both sides"?)
07) -0.075x + (100 - 100) = -6 -- Associative
08) -0.075x + 0 = -6 -- Addition
09) -0.075x = -6 -- Convention
10) 0.075x = 6 -- Property of Equals
11) 6 = 0.075x -- Symmetric Property of Equals

Never doubt the power of basic operations and properties.
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
3,017
This is my first post and I wasn't sure which group to post this in, but this one seems the best fit...if there is a better group, please either move this to that group of ask me to delete and then repost in such and such group. Thanks.

This equation was posted on another site, but it is not available to ask questions on that site, so hoping someone here can help me. The equation was posted as an answer to the question "how much 92.5% pure silver and how much pure (100%) silver needs to be mixed to obtain a 94% mixture with a resultant 100g of the 94% alloy. Here is the solution provided:
Beginning of the solution
We now write an equation relating the amounts of pure silver in the two "input" mixtures and in the "output" mixture:
"x" grams at 92.5% silver + (100-x) grams at 100% = 100g at 94%

(x)(0.925) + (100-x)(1.0) = (100)(0.94)
0.925x + 100 - x = 94
6 = 0.075x
6000 = 75x
6000/75 = x
80 = x
End of solution

I understand most of the equation but do not get how the equation was solved to give 6=0.075x. The rest I can do. Can someone help me get from the second line to the third line...all the rest makes sense. (I think it is the 2 x's that is throwing me).

TIA
I think you are referring to http://mathforum.org/library/drmath/view/53272.html .

There is a new site with some of the same volunteers, where you can still ask questions: https://www.themathdoctors.org/ .

Of course, you can get (and did get) the same answer here that you'd get there.
 

PNGento

New member
Joined
Jan 22, 2019
Messages
3
01) 0.925x + 100 - x = 94
02) 0.925x - x + 100 = 94 -- Commutative
03) (0.925x - x) + 100 = 94 -- Associative
04) (0.925 - 1)*x + 100 = 94 -- Distributive
05) -0.075x+ 100 = 94 -- Addition
06) -0.075x + 100 - 100 = 94 - 100 -- Property of Equals (Is there a formal name for "Do the same thing to both sides"?)
07) -0.075x + (100 - 100) = -6 -- Associative
08) -0.075x + 0 = -6 -- Addition
09) -0.075x = -6 -- Convention
10) 0.075x = 6 -- Property of Equals
11) 6 = 0.075x -- Symmetric Property of Equals

Never doubt the power of basic operations and properties.
Thank you so very much...this I totally understand.
 

PNGento

New member
Joined
Jan 22, 2019
Messages
3

Denis

Senior Member
Joined
Feb 17, 2004
Messages
1,444
General case:
Q : P (Quantity : Percentage)
a : u
b : v
---------
a+b : w
Formula:
w = (au + bv) / (a + b)

Your problem:
a : 100
100-a : 92.5
--------------
100 : 94

94 = (a*100 + (100-a)*92.5) / 100
Solve for a
 
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