To share $\$77$ in a ratio of 4:2:1, I need to divide the money into 4 + 2 + 1 = 7 equal parts. Each part is worth $\frac{77}{7} = \$11$. Carolyn gets 4 parts, so she receives 4 times $\$11$, which is $\$44$. 
Carolyn, Julie and Roberta share $\$77$ in a ratio of 4:2:1,  respectively.  How many dollars did Carolyn receive?