Question

The average of n numbers is 32. If three-fourth of the numbers are increased by 4 and the remaining are decreased by 6, what is the new average?

Answer 1

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Answer 2

The new average is 33.5.

Step-by-step explanation:

Since we have given that

Numbers = n

Average = 32

So, the sum of numbers = $32\times n=32n$

If three fourth of the numbers are increased by 4

So, it becomes,

$\dfrac{3n}{4}\times 4\\\\=3n$

and the remaining are decreased by 6.

So, it becomes,

$\dfrac{n}{4}\times 6\\\\=\dfrac{3n}{2}$

so, the new average would be

$\dfrac{32n+3n-\dfrac{3n}{2}}{n}\\\\=\dfrac{35n-\dfrac{3n}{2}}{n}\\\\=\dfrac{70n-3n}{2n}\\\\=\dfrac{67}{2}\\\\=33.5$

Hence, the new average is 33.5.

# learn more:

The average of n numbers is 32. If three-fourth of the numbers are increased by 4 and the remaining are decreased by 6, what is the new average?

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