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

Algebra.Com
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)   (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 was fully solved.
  • Text form: x*(1.5)+(x-1)*(4.5)=163.5 simplifies to 0=0
  • Cartoon (animation) form:
    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 .
Remove unneeded parentheses around factor highlight_red%28+1.5+%29
It becomes .

Look at .
Remove unneeded parentheses around factor highlight_red%28+4.5+%29
It becomes .

Look at .
Moved these terms to the left highlight_green%28+-163.5+%29
It becomes .

Look at .
Expanded term 4.5 by using associative property on %28x-1%29
It becomes .

Look at .
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes .

Look at .
Added fractions or integers together
It becomes .

Look at .
Factors 1680 and 10 have greatest common factor (GCF) of 10. Reducing fraction.
It becomes .

Look at .
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes .

Look at .
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 .

Look at .
Added fractions or integers together
It becomes .

Look at .
Remove unneeded parentheses around factor highlight_red%28+60+%29,highlight_red%28+1%2F10+%29
It becomes .

Look at .
Factors 60 and 10 have greatest common factor (GCF) of 10. Reducing fraction.
It becomes .

Look at .
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes .

Look at .
Solved linear equation highlight_red%28+6%2Ax-168=0+%29 equivalent to 6*x-168 =0
It becomes .
Result:
This is an equation! Solutions: x=28.

Universal Simplifier and Solver


Done!



RELATED QUESTIONS

Trees are planted at intervals of 10 m along one side of a straight path. The first tree... (answered by Theo)
From the same spot, two runners start running toward opposite directions along the same... (answered by ikleyn)
A flower bed measures 12 m by 5 m and a path of a uniform width runs along one side and... (answered by checkley77)
A rectangular plot measures 12m by 5m. A path of constant width runs along one side and... (answered by ikleyn)
A rectangular garden measures 12m by 5m, a path of uniform width runs along one side and... (answered by mananth,greenestamps)
A rectangular garden measure 12m by 5m a path of uniform widtg runs along one side and... (answered by josgarithmetic)
An object moves along a straight path at a speed v(t) = 2+4t-t2 of m/s. When will the... (answered by ikleyn)
Two cross-country skiers come to a fork on the road. They then split up one to each... (answered by ikleyn)
a park has a 5-foot wide straight path from one end of the park to the other. If the area (answered by stanbon)