SOLUTION: Mona is spinning yarn using different materials. She is combining wool fibers, which cost 45.70$ per kilogram, and acrylic, which costs $15.95 per kilogram. Overall, the finished p

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Question 1157728: Mona is spinning yarn using different materials. She is combining wool fibers, which cost 45.70$ per kilogram, and acrylic, which costs $15.95 per kilogram. Overall, the finished product will cost $27.85 per kilogram. If Mona has 5 kilogram of wool on hand, how many kilograms of the acrylic fiber will she need?
Found 2 solutions by josgarithmetic, Shin123:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
5 kg of wool
x kg of acrylic
x+5 kg of the resulting blend at $27.85

5%2A45.7%2B15.95x=27.85%28x%2B5%29
Solve this equation.

Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
This is the solution to the equation @josgarithmetic,
Solved by pluggable solver: Solve an equation
This is a solution to the equation:
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=7.39583333333333.
  • Graphical form: Equation 5%2A45.7%2B15.95x=27.95%2A%28x%2B5%29 was fully solved.
  • Text form: 5*45.7+15.95x=27.95*(x+5) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+5%2A45.7%2B15.95x=27.95%2A%28x%2B5%29+%29
    For tutors: simplify_cartoon( 5*45.7+15.95x=27.95*(x+5) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+5%2A45.7+%29%2B15.95%2Ax=27.95%2A%28x%2B5%29.
Moved 5%2A45.7 to the right of expression
It becomes 15.95%2Ax%2Bhighlight_green%28+5%2A45.7+%29=27.95%2A%28x%2B5%29.
Look at 15.95%2Ax%2B5%2A45.7=highlight_red%28+27.95%2A%28x%2B5%29+%29.
Moved these terms to the left highlight_green%28+-27.95%2A%28x%2B5%29+%29
It becomes 15.95%2Ax%2B5%2A45.7-highlight_green%28+27.95%2A%28x%2B5%29+%29=0.
Look at 15.95%2Ax%2Bhighlight_red%28+5%2A45.7+%29-27.95%2A%28x%2B5%29=0.
Moved 5%2A45.7 to the right of expression
It becomes 15.95%2Ax-27.95%2A%28x%2B5%29%2Bhighlight_green%28+5%2A45.7+%29=0.
Look at 15.95%2Ax-highlight_red%28+27.95%2A%28x%2B5%29+%29%2B5%2A45.7=0.
Expanded term -27.95 by using associative property on %28x%2B5%29
It becomes 15.95%2Ax-highlight_green%28+27.95%2Ax+%29-highlight_green%28+27.95%2A5+%29%2B5%2A45.7=0.
Look at 15.95%2Ax-27.95%2Ax-highlight_red%28+27.95%2A5+%29%2Bhighlight_red%28+5%2A45.7+%29=0.
Replace constants in expression: highlight_red%28+-27.95%2A5+%29,highlight_red%28+5%2A45.7+%29 with highlight_green%28+88.75+%29
It becomes highlight_green%28+88.75+%29%2B15.95%2Ax-27.95%2Ax=0.
Look at highlight_red%28+88.75+%29%2B15.95%2Ax-27.95%2Ax=0.
Moved 88.75 to the right of expression
It becomes 15.95%2Ax-27.95%2Ax%2Bhighlight_green%28+88.75+%29=0.
Look at highlight_red%28+15.95%2Ax+%29-highlight_red%28+27.95%2Ax+%29%2B88.75=0.
Eliminated similar terms highlight_red%28+15.95%2Ax+%29,highlight_red%28+-27.95%2Ax+%29 replacing them with highlight_green%28+%2815.95-27.95%29%2Ax+%29
It becomes highlight_green%28+%2815.95-27.95%29%2Ax+%29%2B88.75=0.
Look at %28highlight_red%28+15.95+%29-highlight_red%28+27.95+%29%29%2Ax%2B88.75=0.
Added fractions or integers together
It becomes %28-highlight_green%28+1200%2F100+%29%29%2Ax%2B88.75=0.
Look at highlight_red%28+%28-highlight_red%28+1200%2F100+%29%29%2Ax+%29%2B88.75=0.
Remove unneeded parentheses around factor highlight_red%28+1200+%29,highlight_red%28+1%2F100+%29
It becomes -highlight_green%28+1200+%29%2Fhighlight_green%28+100+%29%2Ax%2B88.75=0.
Look at -highlight_red%28+1200+%29%2Fhighlight_red%28+100+%29%2Ax%2B88.75=0.
Factors 1200 and 100 have greatest common factor (GCF) of 100. Reducing fraction.
It becomes -highlight_green%28+12+%29%2Fhighlight_green%28+1+%29%2Ax%2B88.75=0.
Look at -12%2Fhighlight_red%28+1+%29%2Ax%2B88.75=0.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes -12%2Ax%2B88.75=0.
Look at highlight_red%28+-12%2Ax%2B88.75+%29=0.
Solved linear equation highlight_red%28+-12%2Ax%2B88.75=0+%29 equivalent to -12*x+88.75 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=7.39583333333333.

Universal Simplifier and Solver


Done!
0=0;x=7.39583333333333
Subtracting 88.75 from both sides, we get -12x=-88.75. Multiplying both sides by -4, we get 48x=355 So x=355/48, which is approximately 7.395833...