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.
