SOLUTION: A farmer has a 40 ft by 100 ft rectangular field that he wants to reduce to 67.5% of its original size. How wide of a strip should he cut around the edge of his field to do this?
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-> SOLUTION: A farmer has a 40 ft by 100 ft rectangular field that he wants to reduce to 67.5% of its original size. How wide of a strip should he cut around the edge of his field to do this?
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Question 1171007: A farmer has a 40 ft by 100 ft rectangular field that he wants to reduce to 67.5% of its original size. How wide of a strip should he cut around the edge of his field to do this? Answer by ikleyn(53937) (Show Source):
The reduced area (the area after reducing) is 40*100*0.675 = 2700 square feet.
Let x be the uniform width of the strip to cut it around the edge of the field.
Then the new dimensions are (100-2x) feet and (40-2x) feet, and the area equation is
(100-2x)*(40-2x) = 2700 square feet.
Now, the formal way is to reduce it to the standard form quadratic equation
and then solve it using the quadratic formula or factoring.
But you may notice that 2700 = 90*30,
so all you need is to subtract 10 from 100 and 40.
In other words, you mentally guess (with my help) that 2x = 10 feet; hence x= 5 feet is the solution and the answer.
Thus the problem is just solved and the answer is "the strip width is 5 feet".
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From my solution, learn two ways to solve the problem: formal algebraic solving via quadratic equation
and simple way solving it mentally.
