document.write( "Question 880774: Benches are placed 4.5 m apart along a straight path, including one at the start and one at the end of the path. The length of each bench is 1.5 m.\r
\n" ); document.write( "\n" ); document.write( "(a) What is the length of the path with 17 benches?\r
\n" ); document.write( "\n" ); document.write( "(b) How many benches are there along a straight path of 163.5 m?
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Algebra.Com's Answer #531688 by Boyen(12)\"\" \"About 
You can put this solution on YOUR website!
a)
\n" ); document.write( "For explaining purposes :
\n" ); document.write( "Lets say you only wanted to calculate the path of 3 benches, the result would then be :
\n" ); document.write( "1.5 + 4.5 + 1.5 + 4.5 + 1.5 = 13.5
\n" ); document.write( "I could also write this as
\n" ); document.write( "3*(1.5) + 2*(4.5) = 13.5
\n" ); document.write( "Turning this into a formula :
\n" ); document.write( "x*(1.5) + (x-1)*(4.5) = y\r
\n" ); document.write( "\n" ); document.write( "So for 17 benches :
\n" ); document.write( "17 * 1.5 + 16 * 4.5 = 97
\n" ); document.write( "a) the length would be 97 m\r
\n" ); document.write( "\n" ); document.write( "for b)
\n" ); document.write( "x*(1.5) + (x-1)*(4.5) = 163.5\r
\n" ); document.write( "\n" ); document.write( "Using this website's awesome automatic solver :\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=28.
    • \n" ); document.write( "
  • Graphical form: Equation \"x%2A%281.5%29%2B%28x-1%29%2A%284.5%29=163.5\" was fully solved.
  • Text form: x*(1.5)+(x-1)*(4.5)=163.5 simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+x%2A%281.5%29%2B%28x-1%29%2A%284.5%29=163.5+%29\"
    For tutors: simplify_cartoon( x*(1.5)+(x-1)*(4.5)=163.5 )
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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 \"highlight_red%28+x%2A%28highlight_red%28+1.5+%29%29+%29%2B%28x-1%29%2A%284.5%29=163.5\".
Remove unneeded parentheses around factor \"highlight_red%28+1.5+%29\"
It becomes \"x%2Ahighlight_green%28+1.5+%29%2B%28x-1%29%2A%284.5%29=163.5\".
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Look at \"x%2A1.5%2Bhighlight_red%28+%28x-1%29%2A%28highlight_red%28+4.5+%29%29+%29=163.5\".
Remove unneeded parentheses around factor \"highlight_red%28+4.5+%29\"
It becomes \"x%2A1.5%2B%28x-1%29%2Ahighlight_green%28+4.5+%29=163.5\".
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Look at \"x%2A1.5%2B%28x-1%29%2A4.5=highlight_red%28+163.5+%29\".
Moved these terms to the left \"highlight_green%28+-163.5+%29\"
It becomes \"x%2A1.5%2B%28x-1%29%2A4.5-highlight_green%28+163.5+%29=0\".
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Look at \"x%2A1.5%2Bhighlight_red%28+%28x-1%29%2A4.5+%29-163.5=0\".
Expanded term \"4.5\" by using associative property on \"%28x-1%29\"
It becomes \"x%2A1.5%2Bhighlight_green%28+4.5%2Ax+%29-highlight_green%28+4.5%2A1+%29-163.5=0\".
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Look at \"x%2A1.5%2B4.5%2Ax-4.5%2Ahighlight_red%28+1+%29-163.5=0\".
Remove extraneous '1' from product \"highlight_red%28+1+%29\"
It becomes \"x%2A1.5%2B4.5%2Ax-4.5-163.5=0\".
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Look at \"x%2A1.5%2B4.5%2Ax-highlight_red%28+4.5+%29-highlight_red%28+163.5+%29=0\".
Added fractions or integers together
It becomes \"x%2A1.5%2B4.5%2Ax-highlight_green%28+1680%2F10+%29=0\".
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Look at \"x%2A1.5%2B4.5%2Ax-highlight_red%28+1680+%29%2Fhighlight_red%28+10+%29=0\".
Factors 1680 and 10 have greatest common factor (GCF) of 10. Reducing fraction.
It becomes \"x%2A1.5%2B4.5%2Ax-highlight_green%28+168+%29%2Fhighlight_green%28+1+%29=0\".
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Look at \"x%2A1.5%2B4.5%2Ax-168%2Fhighlight_red%28+1+%29=0\".
Remove extraneous '1' from product \"highlight_red%28+1%2F1+%29\"
It becomes \"x%2A1.5%2B4.5%2Ax-168=0\".
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Look at \"highlight_red%28+x%2A1.5+%29%2Bhighlight_red%28+4.5%2Ax+%29-168=0\".
Eliminated similar terms \"highlight_red%28+x%2A1.5+%29\",\"highlight_red%28+4.5%2Ax+%29\" replacing them with \"highlight_green%28+%281.5%2B4.5%29%2Ax+%29\"
It becomes \"highlight_green%28+%281.5%2B4.5%29%2Ax+%29-168=0\".
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Look at \"%28highlight_red%28+1.5+%29%2Bhighlight_red%28+4.5+%29%29%2Ax-168=0\".
Added fractions or integers together
It becomes \"%28highlight_green%28+60%2F10+%29%29%2Ax-168=0\".
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Look at \"highlight_red%28+%28highlight_red%28+60%2F10+%29%29%2Ax+%29-168=0\".
Remove unneeded parentheses around factor \"highlight_red%28+60+%29\",\"highlight_red%28+1%2F10+%29\"
It becomes \"highlight_green%28+60+%29%2Fhighlight_green%28+10+%29%2Ax-168=0\".
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Look at \"highlight_red%28+60+%29%2Fhighlight_red%28+10+%29%2Ax-168=0\".
Factors 60 and 10 have greatest common factor (GCF) of 10. Reducing fraction.
It becomes \"highlight_green%28+6+%29%2Fhighlight_green%28+1+%29%2Ax-168=0\".
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Look at \"6%2Fhighlight_red%28+1+%29%2Ax-168=0\".
Remove extraneous '1' from product \"highlight_red%28+1%2F1+%29\"
It becomes \"6%2Ax-168=0\".
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Look at \"highlight_red%28+6%2Ax-168+%29=0\".
Solved linear equation \"highlight_red%28+6%2Ax-168=0+%29\" equivalent to 6*x-168 =0
It becomes \"highlight_green%28+0+%29=0\".
Result: \"0=0\"
\n" ); document.write( "This is an equation! Solutions: x=28.

Universal Simplifier and Solver

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Done!

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