SOLUTION: A landscaper combines 4 gallons of a 97% gasoline and 3% oil mix with 1/2 gallon of a 98.5% gasoline and 1.5% oil mix. What percent of the combined mixture is gasoline?

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Question 282915: A landscaper combines 4 gallons of a 97% gasoline and 3% oil mix with 1/2 gallon of a 98.5% gasoline and 1.5% oil mix. What percent of the combined mixture is gasoline?
Answer by Deina(147) About Me  (Show Source):
You can put this solution on YOUR website!
The key to this problem is setting up the formula. Notice that they have thrown in some extra numbers that are irrelevant just to throw us off.

We take what we know:
  • 3% oil mix = 4 gallons
  • 1.5% oil mix = 1/2 gallon.
  • the total quantity is 4 1/2 (4.5) gallons
  • The question asks for the final percentage oil mix

That is all we need to solve the problem, so let's lay this out in the format
+pct%28qty%29+%2B+pct%28qty%29+=+pct%28qty%29+:
+3%284%29+%2B+1.5%281%2F2%29+=+x%284.5%29+

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


YOUR ANSWER


  • This is an equation! Solutions: x=2.83333333333333.
  • Graphical form: Equation 3%2A%284%29%2B1.5%2A%280.5%29=x%2A%284.5%29 was fully solved.
  • Text form: 3*(4)+1.5*(0.5)=x*(4.5) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+3%2A%284%29%2B1.5%2A%280.5%29=x%2A%284.5%29+%29
    For tutors: simplify_cartoon( 3*(4)+1.5*(0.5)=x*(4.5) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+3%2A%28highlight_red%28+4+%29%29+%29%2B1.5%2A%280.5%29=x%2A%284.5%29.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes 3%2Ahighlight_green%28+4+%29%2B1.5%2A%280.5%29=x%2A%284.5%29.
Look at 3%2A4%2Bhighlight_red%28+1.5%2A%28highlight_red%28+0.5+%29%29+%29=x%2A%284.5%29.
Remove unneeded parentheses around factor highlight_red%28+0.5+%29
It becomes 3%2A4%2B1.5%2Ahighlight_green%28+0.5+%29=x%2A%284.5%29.
Look at highlight_red%28+3+%29%2Ahighlight_red%28+4+%29%2B1.5%2A0.5=x%2A%284.5%29.
Multiplied numerator integers
It becomes highlight_green%28+12+%29%2B1.5%2A0.5=x%2A%284.5%29.
Look at 12%2Bhighlight_red%28+1.5+%29%2Ahighlight_red%28+0.5+%29=x%2A%284.5%29.
Replaced numbers in term with 0.75
It becomes 12%2Bhighlight_green%28+0.75+%29=x%2A%284.5%29.
Look at highlight_red%28+12+%29%2Bhighlight_red%28+0.75+%29=x%2A%284.5%29.
Added fractions or integers together
It becomes highlight_green%28+1275%2F100+%29=x%2A%284.5%29.
Look at highlight_red%28+1275+%29%2Fhighlight_red%28+100+%29=x%2A%284.5%29.
Factors 1275 and 100 have greatest common factor (GCF) of 25. Reducing fraction.
It becomes highlight_green%28+51+%29%2Fhighlight_green%28+4+%29=x%2A%284.5%29.
Look at 51%2F4=highlight_red%28+x%2A%28highlight_red%28+4.5+%29%29+%29.
Remove unneeded parentheses around factor highlight_red%28+4.5+%29
It becomes 51%2F4=x%2Ahighlight_green%28+4.5+%29.
Look at 51%2F4=highlight_red%28+x%2A4.5+%29.
Moved these terms to the left highlight_green%28+-x%2A4.5+%29
It becomes 51%2F4-highlight_green%28+x%2A4.5+%29=0.
Look at highlight_red%28+51%2F4+%29-x%2A4.5=0.
Moved 51%2F4 to the right of expression
It becomes -x%2A4.5%2Bhighlight_green%28+51%2F4+%29=0.
Look at highlight_red%28+-x%2A4.5%2B51%2F4+%29=0.
Solved linear equation highlight_red%28+-x%2A4.5%2B51%2F4=0+%29 equivalent to -4.5*x+12.75 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=2.83333333333333.

Universal Simplifier and Solver


Done!


So you can see that the final mixture comes out to 2.8 1/3% and bob's your uncle!