Question 495151: Please help me solve this mixture word problem:
A certain mixture consists of acid and water. If 5 gallons of acid is added to the mixture, it willl produce a mixture that is one-half acid and one-half water. If, on the other hand, 5 gallons of water is added, the resulting mixture is one-third acid. How many gallons of acid does the original mixture contain?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A certain mixture consists of acid and water.
If 5 gallons of acid is added to the mixture, it will produce a mixture that is one-half acid and one-half water.
If, on the other hand, 5 gallons of water is added, the resulting mixture is one-third acid.
How many gallons of acid does the original mixture contain?
:
Let x = the decimal value of of the percent acid in the original mixture
Let y = the amt (in gallons of the original mixture)
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write an equation for each statement, based on the amt of acid:
:
"If 5 gallons of acid is added to the mixture, it will produce a mixture that is one-half acid and one-half water."
xy + 5 = .5(y+5)
xy + 5 = .5y + 2.5
xy = .5y + 2.5 - 5
xy = .5y - 2.5
x = 
:
"If, on the other hand, 5 gallons of water is added, the resulting mixture is one-third acid."
xy =  (y+5)
3xy = y + 5
replace x with ; find y
3y() = y + 5
y cancels (fortunately) so we have
3(.5y - 2.5) = y + 5
1.5y - 7.5 = y + 5
1.5y - y = 5 + 7.5
.5y = 12.5
multiply both side by 2
y = 25 gal is the amt of the original mixture
:
:
Find x using x =
x = 
x = 
x = 
x = .4, the original mixture was 40% acid
:
:
See if that checks out in the first statement
If 5 gallons of acid is added to the mixture, it will produce a mixture that is one-half acid and one-half water."
.4(25) + 5 = .5(25 + 5)
10 + 5 = .5(30); confirms our solution
:
:
An interesting problem (Most of them aren't)
Did all this make sense to you? Make an effort to understand each step, ask me in the comment section, if you have a question. C
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