Question

In a certain year, the difference between Mary’s and Jim’s annual salaries was twice the difference between Mary’s and Kate’s annual salaries. If Mary’s annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year?

Answer 1

Answer: Average annual salary of the 3 people is equal to Kate's annual salary.

Step-by-step explanation:

Since we have given that

Difference between Mary's and Jim's annual salaries be m-j

Difference between Mary's and Kate's annual salaries be m-k

According to question, we get that

$m-j=2(m-k)\\\\m-j=2m-2k\\\\2k-j=2m\\\\2k-j=m$

Average annual salary of the 3 people would be

$\dfrac{m+k+j}{3}\\\\=\dfrac{2k-j+j+k}{3}\\\\=\dfrac{3k}{3}\\\\=k$

Hence, average annual salary of the 3 people is equal to Kate's annual salary.