# SOLUTION: How many gallons of a 70% salt solution must be mixed with 60 gallons of a 18% solution to obtain a solution that is 60% salt?

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Question 24136: How many gallons of a 70% salt solution must be mixed with 60 gallons of a 18% solution to obtain a solution that is 60% salt?
You can put this solution on YOUR website!

Call the 70% solution A, and the 18% solution B

Solution B provides you with units of salt in 60 units. For every unit of solution A you add, you get 0.7 units of salt. This is just the definition of percentages.

So, when adding x units of solution A we get units of salt, and we have gallons, so the percentage salt in the finished solution is:

We want this to equal 60%, or 0.6, so we have to solve the equation:

Unfortunately, I'm not clever enough to make the automatic solver, solve that. But if you multiply both sides by and then put it through the automatic solver it works. See below:

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=252. Graphical form: Equation was fully solved.Text form: 10.8+0.7*x=36+0.6*x simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 10.8+0.7*x=36+0.6*x )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Moved to the right of expression
It becomes .

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Moved to the right of expression
It becomes .

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Moved these terms to the left ,
It becomes .

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It becomes .

Look at .
Moved to the right of expression
It becomes .

Look at .
Factors 252 and 10 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes .

Look at .
Eliminated similar terms , replacing them with
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor ,
It becomes .

Look at .
Remove extraneous '1' from product
It becomes .

Look at .
Solved linear equation equivalent to 0.1*x-25.2 =0
It becomes .
Result:
This is an equation! Solutions: x=252.

### Universal Simplifier and Solver

Done!

And you get the answer 252. Don't forget to check it by putting your answer back into the equation!

Hope this helps

Kev