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vladimir1956 [14]
3 years ago
12

the mean of "n" numbers is "x" . if one more is added the mean is "y" . write an algebraic expression for the value of the numbe

r added?​
Mathematics
1 answer:
vaieri [72.5K]3 years ago
3 0

Answer:

yn +y -xn

Step-by-step explanation:

Mean= sum of numbers ÷number of numbers

x= sum of n numbers ÷n

<em>Multiply</em><em> </em><em>both</em><em> </em><em>sides</em><em> </em><em>by</em><em> </em><em>n</em><em>:</em>

xn= sum of n numbers

sum of n numbers= xn -----(1)

Let the number added be a.

After a has been added,

y= (sum of n numbers +a) ÷(n+1)

<em>Multiply</em><em> </em><em>both</em><em> </em><em>sides</em><em> </em><em>by</em><em> </em><em>(</em><em>n</em><em> </em><em>+</em><em>1</em><em>)</em><em>:</em>

y(n +1)= sum of n numbers +a

sum of n numbers= y(n +1) -a -----(2)

Substitute (1) into (2):

xn= y(n +1) -a

<em>Expand</em><em>:</em>

xn= yn +y -a

a= yn +y -xn

<u>Let's check!</u>

Let the numbers be 1, 2, 3 and 4.

mean, x= 10 ÷4= 2.5

n= 4

Let the new number added, a, be 7.

a= 7

mean, y= 17 ÷5= 3.4

a= yn +y -xn

a= 3.4(4) +3.4 -2.5(4)

a= 7

Thus, the expression is true.

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