document.write( "Question 933630: Austin thought he was supposed to mix 3 cans of frozen juice to every five cans of water. Madeline thought you mixed four cans of water to every one can of frozen juice. The real recipe calls for 3 cans of water to every one can of frozen juice. Show how much of Austin's mixture and how much of Madeline's mixture is needed to make the correct juice recipe. \n" ); document.write( "

Algebra.Com's Answer #566956 by ptaylor(2198) $\"\"$ $\"About$

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Austin's mixture is 3/(3+5)=3/8 frozen juice
\n" ); document.write( "Madeline's mixture is 1/(1+4)=1/5 frozen juice
\n" ); document.write( "The real recipe is 1/(1+3)=1/4 frozen juice
\n" ); document.write( "Let x=amount of Austin's mixture needed
\n" ); document.write( "Let y=amount of Madeline's mixture needed
\n" ); document.write( "Now we know that the amount of pure frozen juice that exists before the mixture takes place ((3/8)x+(1/5)y) has to equal the amount of frozen juice in the final mixture ((1/4)(x+y)). Soooo our equation is:
\n" ); document.write( "(3/8)x +(1/5)y=(1/4)(x+y) multiply each term by 40
\n" ); document.write( "15x+8y=10x+10y
\n" ); document.write( "5x=2y
\n" ); document.write( "x=(2/5)y
\n" ); document.write( "So, for every 5 gal of Madeline's mixture, we need (2/5)*5=2 gal of Austin's mixture
\n" ); document.write( "CK
\n" ); document.write( "Let's say Madeline used 40 gal, then Austin would need to use(2/5)*40=16 gal
\n" ); document.write( "(3/8)*16+(1/5)*40=(1/4)*56
\n" ); document.write( "6+8=14
\n" ); document.write( "14=14\r
\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor \n" ); document.write( "

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