document.write( "Question 29475: I've tried and tried to do this problem with no success so here it is:
\n" ); document.write( "A solution of gasoline and oil used for a gas powered weed trimmer is 8% oil. How much gasoline must be added to 3 gallons of this solution to obtain a new solution that is 5% oil? I set it up like this but I know this is wrong.
\n" ); document.write( "0.08X + 0.05(3+x)= 0.05(3) It comes up to 0 \n" ); document.write( "

Algebra.Com's Answer #16279 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
I sympathise
\n" ); document.write( "If you don't get on the right track it can lead you in never ending circles
\n" ); document.write( "I try to write formulas that say exactly what the words say, only in algebra
\n" ); document.write( "I want a symbol for oil. O looks too much like zero, so
\n" ); document.write( "let Q = gallons of oil in the mixture
\n" ); document.write( "notice the amount of oil never changes in this problem
\n" ); document.write( "let G = gallons of gasolione I started out with
\n" ); document.write( "let X = gallons of gasoline I need to add to satisfy problem
\n" ); document.write( "now I can write equations
\n" ); document.write( "[1] $\"Q%2F%28G+%2B+Q%29+=+.08\"$
\n" ); document.write( "that's what the 1st sentence says
\n" ); document.write( "there are 3 gallons of this solution, so
\n" ); document.write( "[2] $\"G+%2B+Q+=+3\"$
\n" ); document.write( "now I have to add gasoline to make a new solution that is 5%
\n" ); document.write( "[3] $\"Q%2F%28%28G+%2B+X%29+%2B+Q%29+=+.05\"$
\n" ); document.write( "Q, the amount of oil doesn't change
\n" ); document.write( "I can substitute [2] direcly into [1]
\n" ); document.write( " $\"Q%2F3+=+.08\"$
\n" ); document.write( "solve for Q
\n" ); document.write( " $\"Q+=+.24\"$
\n" ); document.write( "substitute this value for Q in [2]
\n" ); document.write( " $\"G+%2B+.24+=+3\"$
\n" ); document.write( " $\"G+=+2.76\"$
\n" ); document.write( "now use these values to solve for X in [3]
\n" ); document.write( " $\".24+%2F+%28%282.76+%2B+x%29+%2B+.24%29+=+.05\"$
\n" ); document.write( " $\".24+=+.138+%2B+.05+%2A+X+%2B+.012\"$
\n" ); document.write( " $\".24+=+.15+%2B+.05+%2A+X\"$
\n" ); document.write( " $\".05+%2A+X+=+.09\"$
\n" ); document.write( " $\"X+=+1.8\"$
\n" ); document.write( "so, I have to add 1.8 gallons of gasoline to the mixture to get 5% oil
\n" ); document.write( "check
\n" ); document.write( "[3] $\".24%2F%28%282.76+%2B+1.8%29+%2B+.24%29+=+.05\"$
\n" ); document.write( " $\".24%2F%284.56+%2B+.24%29+=+.05\"$
\n" ); document.write( " $\".24%2F4.8+=+.05\"$
\n" ); document.write( " $\".05+=+.05\"$
\n" ); document.write( "OK
\n" ); document.write( "another thing to check is, if you have 3 unknowns, you need 3 equations
\n" ); document.write( "if I didn't have 3 equations, I'd keep looking until I found them \n" ); document.write( "

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