The average of x numbers is 3x. If (x - 1) is subtracted from each given number. What will be the new average?
(a) 3(x - 1)
(b) 2x + 1
(c) 2x - 1
(d) data inadequate
please solve it with explain
Answers
Answer:
The new average is 2x+1.
Step-by-step explanation:
It is given that average of x number is 3x.
Formula for mean:
Mean=\dfrac{\text{Sum of observations}}{\text{Number of observation}}Mean=
Number of observation
Sum of observations
3x=\dfrac{\text{Sum of observations}}{x}3x=
x
Sum of observations
Multiply both sides by x.
3x^2=Sum of observations3x
2
=Sumofobservations
If x-1 is subtracted from each given number, then (x-1) is subtracted x times from sum of observations.
Sum of observations = 3x^2 - x(x-1)=3x^2-x^2+x=2x^2+x=3x
2
−x(x−1)=3x
2
−x
2
+x=2x
2
+x
The new average is
Mean=\dfrac{2x^2+x}{x}Mean=
x
2x
2
+x
Mean=\dfrac{x(2x+1)}{x}Mean=
x
x(2x+1)
Mean=2x+1Mean=2x+1
Therefore, the new average is 2x+1.
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