SOLUTION: How many gallons of a 7% salt solution must be mixed with 20 gallons of a 13% solution to obtain a 10% solution

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Question 1181853: How many gallons of a 7% salt solution must be mixed with 20 gallons of a 13% solution to obtain a 10% solution
Found 3 solutions by josgarithmetic, greenestamps, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
How many gallons of 7%, g.
7g%2B13%2A20=10%28g%2B20%29
-
7g=10g%2B10%2A20-13%2A20
7g-10g=20%2810-13%29
10g-7g=20%2813-10%29
g%2810-7%29=20%2813-10%29
highlight%28g=20%28%2813-10%29%2F%2810-7%29%29%29-------now just compute this.

g look s like 15 gallons.
The arithmetic should be simple from there.
g=20%283%2F3%29
g=20%2A1
highlight%28g=20%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


10% is exactly halfway between 7% and 13%, so the two ingredients must be mixed in equal amounts.

ANSWER: 20 gallons

The method shown by the other tutor for solving the problem is valid... but their bad arithmetic at the end resulted in a wrong answer.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
How many gallons of a 7% salt solution must be mixed with 20 gallons of a 13% solution to obtain a 10% solution
g look s like 15 gallons. <=== The ANSWER is NOT 15 gallons. 
ERROR again, from one of the MANY error-prone "responders/respondents" in this forum.

The 7%'s volume is being increased by 3% to 10%, while the 13%'s volume is being reduced by 3% to 10%. 

With 1 volume being increased and the other decreased by the same amount, the different concentrations to be mixed will be the same.

Therefore, CORRECT ANSWER: highlight_green%28matrix%281%2C4%2C+20%2C++gallons%2C+of%2C+each%29%29