Problem: A retiring employee receives an annual pension proportional to the square root of the number of years of his service. Had he served a years more, his pension would have been p dollars greater, whereas, had he served b years more (bî€ =a), his pension would have been q dollars greater than the original annual pension. Find his annual pension in terms of a,b,p, and q.
Answer Choices:
A. 2(a−b)p2−q2​
B. 2ab​(p−q)2​
C. 2(ap−bq)ap2−bq2​
D. 2(bp−aq)aq2−bp2​
E. (a−b)(p−q)​
Solution:
Let X be the amount of the annual pension and y the number of years of service. Then with constant of proportionality k,