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?
Answer by kev82(151)   (Show Source): 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
Your Result:


YOUR ANSWER


  • 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=0
  • Cartoon (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 10.8 to the right of expression
It becomes .
Look at .
Moved 36 to the right of expression
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-0.6%2Ax+%29,highlight_green%28+-36+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Moved -252%2F10 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 highlight_red%28+0.7%2Ax+%29,highlight_red%28+-0.6%2Ax+%29 replacing them with highlight_green%28+%280.7-0.6%29%2Ax+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+1+%29,highlight_red%28+1%2F10+%29
It becomes .
Look at .
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes .
Look at .
Solved linear equation highlight_red%28+x%2F10-126%2F5=0+%29 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
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