The ratio is 2:4:9, so we can consider the total parts we are dividing the total as 2+4+9 = 15.
Then, the first person receives 2/15, the second receives 4/15 and the third receives 9/15.
As the total is 75, we can calculate each part as:
[tex]\begin{gathered} p_1=75*\frac{2}{15}=10 \\ \\ p_2=75*\frac{4}{15}=20 \\ \\ p_3=75*\frac{9}{15}=45 \end{gathered}[/tex]Then, the largest share correspond to the third person and is $45.00.
Answer: $45.00
