SOLUTION: The mean of a set of numbers is 150. If one of the numbers is increased by 245, the mean becomes 185. How many numbers are there in the set? A. 4 B. 7 C. 10 D. 13 But why

Question 1035436: The mean of a set of numbers is 150. If one of the numbers is increased by 245, the mean becomes 185. How many numbers are there in the set?
A. 4
B. 7
C. 10
D. 13
But why?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Problem:

The mean of a set of numbers is 150. If one of the numbers is increased by 245, the mean becomes 185. How many numbers are there in the set?

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Steps:

Let
n = number of values
S = sum of the n numbers
M = mean of the n numbers before you increase one of the numbers by 245
P = mean of the n numbers after you increase one of the numbers by 245

To get the mean M, you add up all the values to get S. Then you divide that sum S by n.

M = S/n

"The mean of a set of numbers is 150" tells us that

M = S/n
150 = S/n
150n = S
S = 150n

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"If one of the numbers is increased by 245" then S would turn into S+245. The new mean P would be

mean = (sum of values)/(number of values)
P = (S+245)/n
185 = (S+245)/n ... plug in the new mean 185
185n = S+245
185n = 150n+245 ... replace S with 150n. solve for n
185n-150n = 150n+245-150n
35n = 245
35n/35 = 245/35
n = 7

So there are 7 values in the data set.

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Final Answer: B. 7
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