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 (bξ =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(aβb)p2βq2β
B. 2abβ(pβq)2β
C. 2(apβbq)ap2βbq2β
D. 2(bpβaq)aq2βbp2β
E. (aβb)(pβq)β
Solution:
Let X be the amount of the annual pension and y the number of years of service. Then with constant of proportionality k,