The average of one group of numbers is 4. A second group contains twice as many numbers and has an average of 10. The average of both numbers combined is.

a. 5

b. 6

c. 7

d. 6

e. 9

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- Jul 23rd 2008, 09:02 PM #1

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- Jul 23rd 2008, 09:35 PM #2

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Hello, Abigail!

The average of one group of numbers is 4.

A second group contains twice as many numbers and has an average of 10.

The average of both groups combined is:

. . (a) 5. . (b) 6. . (c) 7. . (d) 8. . (e) 9

The first group has*n*numbers and a total of*T1.*

. . Hence: .(T1)/n .= .4 . → . T1 = 4n .[1]

The second group has*2n*numbers and a total of*T2.*

. . Hence: .(T2)/2n) .= .10 . → . T2 .= .20n .[2]

Add [1] and [2]: .T1 + T2 .= .4n + 20n .= .24n

The total of both groups is: 24n

There are: .n + 2n .= .3n numbers in the two groups.

Therefore, the average of both groups is: .24n/3n .= .**8**. . . answer choice (d)