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I am struggling with answering this question on averages where I have to find the number which the mean was divided by originally to work out the average. This is the question:

The average height of some children was $129.4$ cm. The height of one child was recorded wrongly as $119$ cm. His correct height should be $182$ cm. As a result, the correct average height of the children was $132.4$ cm. How many children were there?

Thank you and help is appreciated

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closed as off-topic by José Carlos Santos, ahulpke, Saad, Namaste, Strants Feb 23 '18 at 0:28

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This is really simple when you think about it. You are trying to figure out how many students there are. Let's call the number of students x. We can also call the sum of every other student n and the total of all the students for the mistaken height would be n+119.

Because we know that the sum of all the students divided by x is your average, the average*x is equal to the total of all students- leading to the equations below.

129.4x=119+n

132.4x=n+182

We can jiggle it about to make this:

129.4x-119=n

This is your everyday similtaneous equation. So what we do is substitute n in our other equation with the formula for n like so:

132.4x=(129.4x-119)+182

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  • $\begingroup$ amWhy did you delete that extra bit? $\endgroup$ – yolo Feb 25 '18 at 12:34
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Let there be $n$ children. We are told that the sum of all the measured heights is $129.4n$. When we correct the height of one child, the sum goes up by $182-119=63$cm so the new total is $129.4n+63$ and the new average is $129.4+\frac {63}n=132.4$. This gives $\frac {63}n=3, n=21$

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  • $\begingroup$ Thank You I understand now how easy this question actually is=-) $\endgroup$ – AspaeringStar7 Feb 22 '18 at 18:35

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