# Weighted factors

• May 27th 2011, 11:20 AM
mathie
Weighted factors
need help on a simple question.
any helps is appreciated. Please find the question attached

Attachment 21607
• May 27th 2011, 02:40 PM
pickslides
Hi there mathie,

Your excel sheet makes sense to me. But the question may lack some context.
• May 27th 2011, 03:06 PM
emakarov
Let $n_a$ and $n_b$ be the non-working years of A and B, respectively, and let $t_a$ and $t_b$ be the total years (non-working plus working) of A and B. Then the share of the non-working years for A is $x_a = n_a / t_a$, and the share for B is $x_b = n_b / t_b$. Finally, the total share is $x = (n_a+n_b) / (t_a+t_b)$.

Thus, $x=(x_at_a+x_bt_b)/(t_a+t_b)=x_a\cdot t_a/(t_a+t_b)+x_b\cdot t_b/(t_a+t_b)$.