document.write( "Question 224039: The manager of a specialty food store combined almonds that cost $4.50 per pound with walnuts that cost $2.50 per pound. How many pounds of each were used to make a 100-pound mixture that costs $3.24 per pound? \n" ); document.write( "
Algebra.Com's Answer #167408 by drj(1380)\"\" \"About 
You can put this solution on YOUR website!
The manager of a specialty food store combined almonds that cost $4.50 per pound with walnuts that cost $2.50 per pound. How many pounds of each were used to make a 100-pound mixture that costs $3.24 per pound?\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let \"x\" be the number of pounds of almonds.\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let \"100-x\" be the number of pounds of walnuts since we have a 100-pound mixture.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let \"4.50x\" be the dollar value of almonds.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Let \"2.50%28100-x%29\" be the dollar value of walnuts.\r
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\n" ); document.write( "\n" ); document.write( "Step 5. Let \"4.50x%2B2.50%28100-x%29=3.24%2A100\" for a one-hundred pound mixture.\r
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\n" ); document.write( "\n" ); document.write( "Step 6. Solve the equation \"4.50x%2B2.50%28100-x%29=3.24%28100%29\" using the following steps\r
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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "


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  • This is an equation! Solutions: x=37.
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  • Graphical form: Equation \"4.50x%2B2.50%2A%28100-x%29=3.24%2A%28100%29\" was fully solved.
  • Text form: 4.50x+2.50*(100-x)=3.24*(100) simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+4.50x%2B2.50%2A%28100-x%29=3.24%2A%28100%29+%29\"
    For tutors: simplify_cartoon( 4.50x+2.50*(100-x)=3.24*(100) )
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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 \"4.50%2Ax%2B2.50%2A%28highlight_red%28+100+%29-x%29=3.24%2A%28100%29\".
Moved \"100\" to the right of expression
It becomes \"4.50%2Ax%2B2.50%2A%28-x%2Bhighlight_green%28+100+%29%29=3.24%2A%28100%29\".
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Look at \"4.50%2Ax%2B2.50%2A%28-x%2B100%29=highlight_red%28+3.24%2A%28highlight_red%28+100+%29%29+%29\".
Remove unneeded parentheses around factor \"highlight_red%28+100+%29\"
It becomes \"4.50%2Ax%2B2.50%2A%28-x%2B100%29=3.24%2Ahighlight_green%28+100+%29\".
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Look at \"4.50%2Ax%2B2.50%2A%28-x%2B100%29=highlight_red%28+3.24%2A100+%29\".
Moved these terms to the left \"highlight_green%28+-3.24%2A100+%29\"
It becomes \"4.50%2Ax%2B2.50%2A%28-x%2B100%29-highlight_green%28+3.24%2A100+%29=0\".
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Look at \"4.50%2Ax%2Bhighlight_red%28+2.50%2A%28-x%2B100%29+%29-3.24%2A100=0\".
Expanded term \"2.50\" by using associative property on \"%28-x%2B100%29\"
It becomes \"4.50%2Ax-highlight_green%28+2.50%2Ax+%29%2Bhighlight_green%28+2.50%2A100+%29-3.24%2A100=0\".
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Look at \"4.50%2Ax-2.50%2Ax%2Bhighlight_red%28+2.50%2A100+%29-highlight_red%28+3.24%2A100+%29=0\".
Replace constants in expression: \"highlight_red%28+2.50%2A100+%29\",\"highlight_red%28+-3.24%2A100+%29\" with \"highlight_green%28+-74+%29\"
It becomes \"highlight_green%28+-74+%29%2B4.50%2Ax-2.50%2Ax=0\".
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Look at \"highlight_red%28+-74+%29%2B4.50%2Ax-2.50%2Ax=0\".
Moved \"-74\" to the right of expression
It becomes \"4.50%2Ax-2.50%2Ax%2Bhighlight_green%28+-74+%29=0\".
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Look at \"4.50%2Ax-2.50%2Ax%2Bhighlight_red%28+-74+%29=0\".
Removed extra sign in front of \"-74\"
It becomes \"4.50%2Ax-2.50%2Ax-highlight_green%28+74+%29=0\".
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Look at \"highlight_red%28+4.50%2Ax+%29-highlight_red%28+2.50%2Ax+%29-74=0\".
Eliminated similar terms \"highlight_red%28+4.50%2Ax+%29\",\"highlight_red%28+-2.50%2Ax+%29\" replacing them with \"highlight_green%28+%284.50-2.50%29%2Ax+%29\"
It becomes \"highlight_green%28+%284.50-2.50%29%2Ax+%29-74=0\".
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Look at \"%28highlight_red%28+4.50+%29-highlight_red%28+2.50+%29%29%2Ax-74=0\".
Added fractions or integers together
It becomes \"%28highlight_green%28+200%2F100+%29%29%2Ax-74=0\".
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Look at \"highlight_red%28+%28highlight_red%28+200%2F100+%29%29%2Ax+%29-74=0\".
Remove unneeded parentheses around factor \"highlight_red%28+200+%29\",\"highlight_red%28+1%2F100+%29\"
It becomes \"highlight_green%28+200+%29%2Fhighlight_green%28+100+%29%2Ax-74=0\".
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Look at \"highlight_red%28+200+%29%2Fhighlight_red%28+100+%29%2Ax-74=0\".
Factors 200 and 100 have greatest common factor (GCF) of 100. Reducing fraction.
It becomes \"highlight_green%28+2+%29%2Fhighlight_green%28+1+%29%2Ax-74=0\".
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Look at \"2%2Fhighlight_red%28+1+%29%2Ax-74=0\".
Remove extraneous '1' from product \"highlight_red%28+1%2F1+%29\"
It becomes \"2%2Ax-74=0\".
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Look at \"highlight_red%28+2%2Ax-74+%29=0\".
Solved linear equation \"highlight_red%28+2%2Ax-74=0+%29\" equivalent to 2*x-74 =0
It becomes \"highlight_green%28+0+%29=0\".
Result: \"0=0\"
\n" ); document.write( "This is an equation! Solutions: x=37.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "With x=37 and 100-x=63, check dollar value...4.50*37+2.50*63=324 dollars for a 100 pound mixture which is a true statement.\r
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\n" ); document.write( "\n" ); document.write( "Step 7. ANSWER: The amount of almonds is 37 pounds and the amount of walnuts is 63 pounds.\r
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\n" ); document.write( "\n" ); document.write( "I hope the above steps and explanation were helpful. \r
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\n" ); document.write( "\n" ); document.write( "For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry. \r
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\n" ); document.write( "\n" ); document.write( "Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.\r
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\n" ); document.write( "\n" ); document.write( "Respectfully,
\n" ); document.write( "Dr J\r
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\n" ); document.write( "\n" ); document.write( "http://www.FreedomUniversity.TV\r
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