How many gallons of a 12%-salt sodium must be mixed with....

[fathauer]

How many gallons of a 12%-salt sodium must be mixed with 6 gallons of a 20%-salt sodium to obtain a 15%-salt sodium?

I have no idea how to set the problem up. The examples in the book are very different.

Thank you!

 

[galactus]

Think about it.

The amount of salt is the strength times the gallons.
Therefore, 6 gallons of mixture that is 20% salt has 1.2 gallon of salt in it.
It would be 4.8 gallon of water(or some other medium) and 1.2 gallon of salt.

Make a table:

# gallons        strength      amount of salt.
------------    --------------   -----------------
   6                  20%            0.20(6)
   x                  12%            0.12x
   x+6              15%            0.15(6+x)

 

[arthur ohlsten]

let S be the gallons of salt solution
then gallons of salt from this solution is
.12 S = gals salt

we have 6 gallons of a 20% salt solution
gals of salt from this solution is
.2[6] gals salt

total volume of liqid is: [6+S] gallons

amount salt in this volume is 15%

.15[S+6]=.12S+.2[6]
.15S +.9=.12S+1.2
.03S=.3
S=10 gallons answer

 

[fathauer]

huge help! thank you

 

[arthur ohlsten]

your welcome.
please check my work for possible errors, we all make them
Arthur