SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given ratios
[tex]\begin{gathered} Erin=\frac{3}{7} \\ \\ Kim=5 \\ \\ Megan=\frac{1}{3} \end{gathered}[/tex]STEP 2: Add the ratios
[tex]\begin{gathered} \frac{3}{7}+5+\frac{1}{3} \\ =\frac{3}{7}+\frac{5}{1}+\frac{1}{3} \\ =\frac{9}{21}+\frac{105}{21}+\frac{7}{21} \\ =\frac{9+105+7}{21} \\ =\frac{121}{21} \end{gathered}[/tex]STEP 3: Calculate the earnings of each of them
Erin's
[tex]\begin{gathered} \frac{Erin^{\prime}s\text{ ratio}}{Total\text{ ratio}}\cdot Total\text{ winnings} \\ \\ By\text{ substitution,} \\ \frac{\frac{3}{7}}{\frac{121}{21}}\cdot14780=\frac{3}{7}\cdot\frac{21}{121}\cdot14780=\frac{133020}{121}=\:1099.33884\approx\text{ \$}1099.34 \end{gathered}[/tex]Kim's
[tex]\begin{gathered} \frac{5}{\frac{121}{21}}\cdot14780 \\ =5\div\frac{121}{21}\cdot14780=5\cdot\frac{21}{121}\cdot14780=\frac{1551900}{121}=\:12825.61983\approx\text{ \$}12825.62 \end{gathered}[/tex]Megans's
[tex]\begin{gathered} \frac{1}{3}\div\frac{121}{21}\cdot14780 \\ \frac{1}{3}\cdot\frac{21}{121}\cdot14780=\frac{103460}{121}=855.04132\approx\text{\$}855.04 \end{gathered}[/tex]Hence, the earnings are given as:
Erin's: $1099.34
Kim's: $12825.62
Megan's: $855.04