SOLUTION: the length of a rectangle is 8 m more than 6 times the width. the perimeter is 156 m. find the width.

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Question 222921: the length of a rectangle is 8 m more than 6 times the width. the perimeter is 156 m. find the width.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is 8 m more than 6 times the width. The perimeter is 156 m. Find the width.

Step 1. Perimeter P means adding up all the lengths of the sides of a rectangle.

Step 2. Let w be the width.

Step 3. Let 6w+8 be the length.

Step 4. Then P=w+w+6w+8+6w+8=156 m.

Step 5. Solving the equation in Step 4 leads to the following steps:

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


YOUR ANSWER


  • This is an equation! Solutions: w=10.
  • Graphical form: Equation w%2Bw%2B6w%2B8%2B6w%2B8=156 was fully solved.
  • Text form: w+w+6w+8+6w+8=156 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+w%2Bw%2B6w%2B8%2B6w%2B8=156+%29
    For tutors: simplify_cartoon( w+w+6w+8+6w+8=156 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at w%2Bw%2B6%2Aw%2Bhighlight_red%28+8+%29%2B6%2Aw%2Bhighlight_red%28+8+%29=156.
Added fractions or integers together
It becomes w%2Bw%2B6%2Aw%2Bhighlight_green%28+16+%29%2B6%2Aw=156.
Look at w%2Bw%2B6%2Aw%2Bhighlight_red%28+16+%29%2B6%2Aw=156.
Moved 16 to the right of expression
It becomes w%2Bw%2B6%2Aw%2B6%2Aw%2Bhighlight_green%28+16+%29=156.
Look at .
Eliminated similar terms highlight_red%28+w+%29,highlight_red%28+w+%29,highlight_red%28+6%2Aw+%29,highlight_red%28+6%2Aw+%29 replacing them with highlight_green%28+%281%2B1%2B6%2B6%29%2Aw+%29
It becomes highlight_green%28+%281%2B1%2B6%2B6%29%2Aw+%29%2B16=156.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+14+%29%29%2Aw%2B16=156.
Look at highlight_red%28+%28highlight_red%28+14+%29%29%2Aw+%29%2B16=156.
Remove unneeded parentheses around factor highlight_red%28+14+%29
It becomes highlight_green%28+14+%29%2Aw%2B16=156.
Look at 14%2Aw%2B16=highlight_red%28+156+%29.
Moved these terms to the left highlight_green%28+-156+%29
It becomes 14%2Aw%2B16-highlight_green%28+156+%29=0.
Look at 14%2Aw%2Bhighlight_red%28+16+%29-highlight_red%28+156+%29=0.
Added fractions or integers together
It becomes 14%2Aw%2Bhighlight_green%28+-140+%29=0.
Look at 14%2Aw%2Bhighlight_red%28+-140+%29=0.
Removed extra sign in front of -140
It becomes 14%2Aw-highlight_green%28+140+%29=0.
Look at highlight_red%28+14%2Aw-140+%29=0.
Solved linear equation highlight_red%28+14%2Aw-140=0+%29 equivalent to 14*w-140 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=10.

Universal Simplifier and Solver


Done!



With w=10, then 6w+8=68 and P=2(10+68)=156... which is a true statement.

Step 6. ANSWER: Width is 10 meters.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J