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 hasnnumbers and a total ofT1.

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

The second group has2nnumbers and a total ofT2.

. . 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)