The number of males M (in thousands)and the number of females F (in thousands)participating in high school athletic programs from 1995 through 2001 can be modeled by $M = \frac { 463.76 t + 2866.4 } { 0.09 t + 1.0 }$ and $F = \frac { 3183.41 t - 4762.2 } { t }$. In these models, t represents the year, with t=5 corresponding to 1995. Find a rational model that represents the total number T of participants in high school athletic programs.
A) $\frac { 2719.65 t + 1895.8 } { 0.91 t + 1.0 }$
B) $\frac { 750.27 t ^ { 2 } + 5621.212 t - 4762.2 } { t ( 0.09 t + 1.0 ) }$
C) $\frac { 463.76 t ^ { 2 } + 1895.8 t - 7628.6 } { t ( 0.09 t + 1.0 ) }$
D) $\frac { 3647.17 t - 7628.6 } { 1.09 t + 1.0 }$
E) $\frac { 3183.41 t ^ { 2 } + 7628.6 t - 1895.8 } { t ( 0.09 t + 1.0 ) }$

Question

Quizplus · Accepted Answer

To find the total number of participants T, we add the models for M and F: $T = M + F = \frac { 463.76 t + 2866.4 } { 0.09 t + 1.0 } + \frac { 3183.41 t - 4762.2 } { t }$. Simplifying this expression to a common denominator gives us the model in choice B.

The Number of Males M (In Thousands)and the Number of Females