Question

the mean of a set of five numbers is 3k. when a sixth number is added to the set, the mean increases by k. what is the ratio of the sixth number to the sum of the first five numbers? express your answer as a common fraction.

Answer 1

Let’s call the sum of the set of five numbers S and the sixth number N. We know the mean of the set of five numbers is 3k, so we can write the equation S/5 = 3k or S = 15k. When we add the sixth number the mean increases by k, so we can write the equations (S + N)/6 = 4k or S + N = 24k. Using S = 15k, we find that N = 9k. The ratio of the sixth number to the sum of the set of five numbers is therefore N/S = 9k/15k = 3/5.