document.write( "Question 282915: A landscaper combines 4 gallons of a 97% gasoline and 3% oil mix with 1/2 gallon of a 98.5% gasoline and 1.5% oil mix. What percent of the combined mixture is gasoline? \n" ); document.write( "
Algebra.Com's Answer #205468 by Deina(147)\"\" \"About 
You can put this solution on YOUR website!
The key to this problem is setting up the formula. Notice that they have thrown in some extra numbers that are irrelevant just to throw us off.
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  • 3% oil mix = 4 gallons
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  • 1.5% oil mix = 1/2 gallon.
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  • the total quantity is 4 1/2 (4.5) gallons
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  • The question asks for the final percentage oil mix
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\n" ); document.write( "\n" ); document.write( "That is all we need to solve the problem, so let's lay this out in the format
\n" ); document.write( "\"+pct%28qty%29+%2B+pct%28qty%29+=+pct%28qty%29+\":
\n" ); document.write( "\"+3%284%29+%2B+1.5%281%2F2%29+=+x%284.5%29+\"

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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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  • This is an equation! Solutions: x=2.83333333333333.
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  • Graphical form: Equation \"3%2A%284%29%2B1.5%2A%280.5%29=x%2A%284.5%29\" was fully solved.
  • Text form: 3*(4)+1.5*(0.5)=x*(4.5) simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+3%2A%284%29%2B1.5%2A%280.5%29=x%2A%284.5%29+%29\"
    For tutors: simplify_cartoon( 3*(4)+1.5*(0.5)=x*(4.5) )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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Look at \"highlight_red%28+3%2A%28highlight_red%28+4+%29%29+%29%2B1.5%2A%280.5%29=x%2A%284.5%29\".
Remove unneeded parentheses around factor \"highlight_red%28+4+%29\"
It becomes \"3%2Ahighlight_green%28+4+%29%2B1.5%2A%280.5%29=x%2A%284.5%29\".
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Look at \"3%2A4%2Bhighlight_red%28+1.5%2A%28highlight_red%28+0.5+%29%29+%29=x%2A%284.5%29\".
Remove unneeded parentheses around factor \"highlight_red%28+0.5+%29\"
It becomes \"3%2A4%2B1.5%2Ahighlight_green%28+0.5+%29=x%2A%284.5%29\".
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Look at \"highlight_red%28+3+%29%2Ahighlight_red%28+4+%29%2B1.5%2A0.5=x%2A%284.5%29\".
Multiplied numerator integers
It becomes \"highlight_green%28+12+%29%2B1.5%2A0.5=x%2A%284.5%29\".
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Look at \"12%2Bhighlight_red%28+1.5+%29%2Ahighlight_red%28+0.5+%29=x%2A%284.5%29\".
Replaced numbers in term with 0.75
It becomes \"12%2Bhighlight_green%28+0.75+%29=x%2A%284.5%29\".
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Look at \"highlight_red%28+12+%29%2Bhighlight_red%28+0.75+%29=x%2A%284.5%29\".
Added fractions or integers together
It becomes \"highlight_green%28+1275%2F100+%29=x%2A%284.5%29\".
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Look at \"highlight_red%28+1275+%29%2Fhighlight_red%28+100+%29=x%2A%284.5%29\".
Factors 1275 and 100 have greatest common factor (GCF) of 25. Reducing fraction.
It becomes \"highlight_green%28+51+%29%2Fhighlight_green%28+4+%29=x%2A%284.5%29\".
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Look at \"51%2F4=highlight_red%28+x%2A%28highlight_red%28+4.5+%29%29+%29\".
Remove unneeded parentheses around factor \"highlight_red%28+4.5+%29\"
It becomes \"51%2F4=x%2Ahighlight_green%28+4.5+%29\".
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Look at \"51%2F4=highlight_red%28+x%2A4.5+%29\".
Moved these terms to the left \"highlight_green%28+-x%2A4.5+%29\"
It becomes \"51%2F4-highlight_green%28+x%2A4.5+%29=0\".
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Look at \"highlight_red%28+51%2F4+%29-x%2A4.5=0\".
Moved \"51%2F4\" to the right of expression
It becomes \"-x%2A4.5%2Bhighlight_green%28+51%2F4+%29=0\".
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Look at \"highlight_red%28+-x%2A4.5%2B51%2F4+%29=0\".
Solved linear equation \"highlight_red%28+-x%2A4.5%2B51%2F4=0+%29\" equivalent to -4.5*x+12.75 =0
It becomes \"highlight_green%28+0+%29=0\".
Result: \"0=0\"
\n" ); document.write( "This is an equation! Solutions: x=2.83333333333333.

Universal Simplifier and Solver

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Done!
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\n" ); document.write( "So you can see that the final mixture comes out to 2.8 1/3% and bob's your uncle! \n" ); document.write( "
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