SOLUTION: A boy measures a road as being 69.3km long, however, there is a -1% error in this measurement. What is the true length of the road?

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Question 1145441: A boy measures a road as being 69.3km long, however, there is a -1% error in this measurement. What is the true length of the road?
Found 3 solutions by CubeyThePenguin, greenestamps, ikleyn:
Answer by CubeyThePenguin(3113)   (Show Source): You can put this solution on YOUR website!
true length: (69.3) * 101% = 69.993 km
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Another hastily composed and incorrect response from tutor @CubeyThePenguin....

An error of -1% in the measurement means the measured length was 99% of the actual length. So the actual length was 69.3/0.99 = 70 (exactly).

The other tutor's calculation was 69.3*1.01 = 69.993, which he rounded off to 70.

The difference between the two answers is small; but in a similar problem where the error was 10% or even 20%, the differences would be significant.
Answer by ikleyn(52807)   (Show Source): You can put this solution on YOUR website!
.

Let x be the ACTUAL length of the road.


Then the problem says


    x - 0.01x = 69.3  kilometers.

or

    0.99x = 69.3  kilometers.


Then the actual length is   = 70.00000000000 kilometers.      ANSWER

Solved.


------------


It is the correct answer and correct treatment of the problem.


The treatment in the post by  @CubeyThePenguin is  NOT  CORRECT.


Notice that his number of     is  69.993 kilometers ------   NOT  70  kilometers.


Also notice that this problem is not about treating of several centimeters or millimeters of the road -

it is about using the  Math conceptions properly.


It is why  I  have written my post.



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