SOLUTION: Write an equation and solve. Using guess & check method only. The width of Henry's pool is 8 yards less than its length. If the area of the pool is 200 square yards, what a

Question 313288: Write an equation and solve. Using guess & check method only.
The width of Henry's pool is 8 yards less than its length. If the area of the pool is 200 square yards, what are its length and width?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
The formula for the area of a rectangle is L * W = A

Since the width of the pool is 8 yards less than its length, we get:

L = Length of Pool
W = L - 8 = Width of Pool

We know the area of the pool is 200 square yards.

This means that L * W = 200

Since we also know that W = L - 8, then this formula becomes:

L * (L - 8) = 200

We simplify this formula to get:

L^2 - 8*L = 200

We subtract 200 from both sides of this equation to get:

L^2 - 8*L - 200 = 0

From here we could solve the quadratic equation or we could do guess and check.

In order to do guess and check, we'll go back to:

L^2 - 8*L = 200 since solving for that is one step less.

Allow L = 10 to start with.

You get 100 - 80 = 200 which becomes 120 = 200 which is way too low.

Double L to 20.

You get 400 - 160 = 200 which becomes 240 = 200 which is a little too high.

Since L = 20 was a lot closer to 200 then L = 10, your answer will probably be much closer to 20 than to 10.

Try 18 for L to get 324 - 144 = 200 which becomes 180 = 200. Still a little too low.

Try 19 for L to get 361 - 152 = 200 which becomes 209 = 200. Just a little too high.

Your answer is going to be between 18 and 19.

It will probably be closer to 19 rather than 18 because 19 was only 9 off from 200 while 18 was 20 off.

Try 18.8 for L to get 203.04 = 200 which is a little too high.

Try 18.7 for L to get 200.09 = 200 which is very close, but still too high.

Since it's still too high, you would probably go down to 18.6 to get 197.16 = 200 which means you're too low.

Your answer will be between 18.6 and 18.7 and will probably be closer to 18.7 because 18.7 was .09 off while 18.6 was 2.84 off.

You would probably then try 18.68 to get 199.5024 = 200 which is still closer but still too low.

You would probably then try 18.69 to get 199.7961 which is even closer to 200 but still low.

Since 18.69 is too low and 18.7 is too high, then the answer has to be between 18.69 and 18.7.

since 18.7 is .09 too high and 18.69 is .2039 too low, then the answer is probably going to be closer to 18.7 than 18.69.

My guess is your answer will be close to 18.697. That would get you 200.001809 which is very close.

We could narrow it down further, but this looks close enough.

If you solved the quadratic equation of L^2 - 8*l - 200 = 0, you would get:

L = 18.69693846

We did pretty good through guess and check.

Once you know L, it's a simple matter to find W.

W = L - 8

L = 18.69693846 (the real answer, not the one we guessed at).
W = 10.69693846

L * W = 18.69693846 * 10.69693846 = 200

Using our guess, we would have gotten:

L = 18.697 and W = L - 8 = 10.697

L * W = 200 would become 18.697 * 10.697 = 200.001809.

Not too shabby.

The guess and check method is used in a lot of cases where a formula is not possible.

It lends itself very well to computers which can do the calculations extremely fast.

You can also use interpolation to narrow your next guess down closer.

I did some of that by recognizing that the answer with L = 10 was much further away than the answer with L = 20 which led me to conclude that the answer was probably going to be somewhere between 18.8 and 20.

I was a little off but not too far since the real answer was 18.697.

With computers, the interpolation method would be by formula rather than guess work.

My third guess would have been x = 18.1818181818 if I used an interpolation formula.

This wasn't too far off from my third guess of 18.

Guess and Check is a laborious process that computers do extremely well.

It's used in a lot of cases where solving by formula directly is just not possible.

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