SOLUTION: The average of 6 numbers is -24. If we add 1 more number the average becomes -21. Find the new number and show workings. Thanks.

Since the average of the 6 numbers is -24, the sum of these 6 numbers is 6*(-24) = -144.


Since the average of the 7 numbers is -21, the sum of these 7 numbers is 7*(-21) = -147.


Hence, the 7-th number is the difference of -147 and -144, which is equal to 

       -147 - (-144) = -147 + 144 = -3.


ANSWER.  The 7-th number is -3.