# math word problem

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A rectangle garden is 30 ft by 40 ft. Part of the garden is removed in order to install a walkway of uniform width around it. The area of the new garden is one-half the area of the old garden. How wide is the walkway?

• math word problem -

Let the walkway have width w
The new dimensions of the garden are

(30-2w) x (40-2w)

That's half of the original area, 30x40

(30-2w)(40-2w) = 1/2 * 30*40
1200 - 140w + 4w^2 = 600
4w^2 - 140w + 600 = 0
w^2 - 35w + 150 = 0
(w-5)(w-30) = 0

w=30 doesn't make much sense. No garden left
w=5 means that the new garden is

20x30 = 1/2 of 30x40

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