Chapter 6.4A, Problem 22A

a. In Room A, there are 1 man and 2 women; in Room B, there are 2 men and 4 women; and in Room C, there are 5 men and 10 women. If all the people in Rooms B and C go to Room A, what will be the ratio of men to women in Room A?

b. Prove the following generalization of the proportions used in part (a).

If $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}$ then $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\frac{a+b+c}{b+d+f}$.