SOLUTION: 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. (a) What is the length of the

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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.
(a) What is the length of the path with 17 benches?
(b) How many benches are there along a straight path of 163.5 m?
Answer by Boyen(12) About Me  (Show Source):
You can put this solution on YOUR website!
a)
For explaining purposes :
Lets say you only wanted to calculate the path of 3 benches, the result would then be :
1.5 + 4.5 + 1.5 + 4.5 + 1.5 = 13.5
I could also write this as
3*(1.5) + 2*(4.5) = 13.5
Turning this into a formula :
x*(1.5) + (x-1)*(4.5) = y
So for 17 benches :
17 * 1.5 + 16 * 4.5 = 97
a) the length would be 97 m
for b)
x*(1.5) + (x-1)*(4.5) = 163.5
Using this website's awesome automatic solver :
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=28.
  • 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 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
This is an equation! Solutions: x=28.

Universal Simplifier and Solver


Done!