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K M

Simple Word Problem- Double check answer?

K M
Posted 8 years ago
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Hello, I was just wondering if someone can double check my answer on this word problem. Thank you.

You have a rectangular garden that is 25ft by 11ft. You want to build a pathway around the garden. However, you only have enough gravel to build 576 ft. So, how wide can your pathway around the garden be?

What I did was find the perimeter. P=72 ft

So, then I just divided 576 by 72 and I got 8. My answer was that the pathway had to be 8 ft wide. Is that correct?
POSTED BY: K M
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Paul Cleary
Paul Cleary
Posted 8 years ago

Alternatively we could do it this way, look at diagram

2 (11 * x) + 2 (25 * x) + 4 x^2 = 576

giving

4 x^2 + 72 x - 576 = 0

We could simplify it to

x^2 + 18 x - 144 = 0

Solve either by hand or

Solve[x^2 + 18 x - 144 == 0, x]
{{x -> -24}, {x -> 6}}

and clearly x can't be -24 so there you have the answer.

enter image description here

Paul.
POSTED BY: Paul Cleary

For a path of width w the total area (path plus enclosed area) is (25+2w)(11+2*w) and the enclosed area is (25)(11). The difference is given as 576.

eqn = (25 + 2 w)*(11 + 2 w) - (25*11) == 576;

soln = Solve[{eqn, w > 0}, w][[1]]

{w -> 6}

eqn /. soln

True

So the path is 6 ft wide.
POSTED BY: Robert Hanlon
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