SOLUTION: A man mows his 25 foot by 200 foot rectangular lawn in a spiral pattern starting from the outside edge. After a bit of hard work he stops for a water break he is 82% done. How wide

Question 1166545: A man mows his 25 foot by 200 foot rectangular lawn in a spiral pattern starting from the outside edge. After a bit of hard work he stops for a water break he is 82% done. How wide of a strip has he mowed around the outside edge?
Found 2 solutions by solver91311, greenestamps:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The total area is 200 times 25 square feet. If he is 82% done, he has 18% remaining. So the amount remaining is . Let's call that quantity .

If is the dimension of the width of the strip mowed, then the dimensions of the unmowed portion must be and , so the area of the unmowed portion which we know has a value of must be:

So all that is left is to calculate the value of , expand the product of the two binomials, put the quadratic into standard form, and solve for

John

My calculator said it, I believe it, that settles it

I > Ø

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

This is an example of a problem that is solved far more easily informally than with formal algebra. So I will explain what I would do if I were working this problem and a formal algebraic solution was required.

82% done means 18% remains; 18% of 200*25 feet is 900 square feet. If the width of the strip is x, then

UGH! That looks REALLY nasty....

Instead of trying to factor that, I would stop at this point and solve the problem with logical reasoning and some simple mental arithmetic; then come back to my formal algebraic solution.

width 5 --> 190*15 = 2850
width 10 --> 180*5 = 900

AHA! the answer is 10.

So now back to the formal algebra.

The second possible solution is rejected, since it makes no sense in the original problem.

ANSWER: The strip is 10 feet wide.

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