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) About Me  (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 0.18%2A60=10.8 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 10.8+%2B+0.7x units of salt, and we have 60%2Bx gallons, so the percentage salt in the finished solution is:


%2810.8%2B0.7x%29%2F%2860%2Bx%29

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


%2810.8%2B0.7x%29%2F%2860%2Bx%29=0.6

Unfortunately, I'm not clever enough to make the automatic solver, solve that. But if you multiply both sides by 60%2Bx 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 10.8%2B0.7%2Ax=36%2B0.6%2Ax was fully solved.
  • Text form: 10.8+0.7*x=36+0.6*x simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+10.8%2B0.7%2Ax=36%2B0.6%2Ax+%29
    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 highlight_red%28+10.8+%29%2B0.7%2Ax=36%2B0.6%2Ax.
Moved 10.8 to the right of expression
It becomes 0.7%2Ax%2Bhighlight_green%28+10.8+%29=36%2B0.6%2Ax.
Look at 0.7%2Ax%2B10.8=highlight_red%28+36+%29%2B0.6%2Ax.
Moved 36 to the right of expression
It becomes 0.7%2Ax%2B10.8=0.6%2Ax%2Bhighlight_green%28+36+%29.
Look at 0.7%2Ax%2B10.8=highlight_red%28+0.6%2Ax%2B36+%29.
Moved these terms to the left highlight_green%28+-0.6%2Ax+%29,highlight_green%28+-36+%29
It becomes 0.7%2Ax%2B10.8-highlight_green%28+0.6%2Ax+%29-highlight_green%28+36+%29=0.
Look at 0.7%2Ax%2Bhighlight_red%28+10.8+%29-0.6%2Ax-highlight_red%28+36+%29=0.
Added fractions or integers together
It becomes 0.7%2Ax-highlight_green%28+252%2F10+%29-0.6%2Ax=0.
Look at 0.7%2Ax-highlight_red%28+252%2F10+%29-0.6%2Ax=0.
Moved -252%2F10 to the right of expression
It becomes 0.7%2Ax-0.6%2Ax-highlight_green%28+252%2F10+%29=0.
Look at 0.7%2Ax-0.6%2Ax-highlight_red%28+252+%29%2Fhighlight_red%28+10+%29=0.
Factors 252 and 10 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes 0.7%2Ax-0.6%2Ax-highlight_green%28+126+%29%2Fhighlight_green%28+5+%29=0.
Look at highlight_red%28+0.7%2Ax+%29-highlight_red%28+0.6%2Ax+%29-126%2F5=0.
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 highlight_green%28+%280.7-0.6%29%2Ax+%29-126%2F5=0.
Look at %28highlight_red%28+0.7+%29-highlight_red%28+0.6+%29%29%2Ax-126%2F5=0.
Added fractions or integers together
It becomes %28highlight_green%28+1%2F10+%29%29%2Ax-126%2F5=0.
Look at highlight_red%28+%28highlight_red%28+1%2F10+%29%29%2Ax+%29-126%2F5=0.
Remove unneeded parentheses around factor highlight_red%28+1+%29,highlight_red%28+1%2F10+%29
It becomes highlight_green%28+1+%29%2Fhighlight_green%28+10+%29%2Ax-126%2F5=0.
Look at highlight_red%28+1+%29%2F10%2Ax-126%2F5=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes x%2F10-126%2F5=0.
Look at highlight_red%28+x%2F10-126%2F5+%29=0.
Solved linear equation highlight_red%28+x%2F10-126%2F5=0+%29 equivalent to 0.1*x-25.2 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
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