SOLUTION: 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 mixtu

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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?
Answer by drj(1380) About Me  (Show Source):
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?

Step 1. Let x be the number of pounds of almonds.

Step 2. Let 100-x be the number of pounds of walnuts since we have a 100-pound mixture.

Step 3. Let 4.50x be the dollar value of almonds.

Step 4. Let 2.50%28100-x%29 be the dollar value of walnuts.

Step 5. Let 4.50x%2B2.50%28100-x%29=3.24%2A100 for a one-hundred pound mixture.

Step 6. Solve the equation 4.50x%2B2.50%28100-x%29=3.24%28100%29 using the following steps

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


YOUR ANSWER


  • This is an equation! Solutions: x=37.
  • 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) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
This is an equation! Solutions: x=37.

Universal Simplifier and Solver


Done!



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.

Step 7. ANSWER: The amount of almonds is 37 pounds and the amount of walnuts is 63 pounds.

I hope the above steps and explanation were helpful.

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.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J

http://www.FreedomUniversity.TV