Question

Calculate how much each should receive from the winningsA) Erin’s $ B) Kim’s $ C) Megan’s $

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given ratios

$\begin{gathered} Erin=\frac{3}{7} \\ \\ Kim=5 \\ \\ Megan=\frac{1}{3} \end{gathered}$

STEP 2: Add the ratios

$\begin{gathered} \frac{3}{7}+5+\frac{1}{3} \\ =\frac{3}{7}+\frac{5}{1}+\frac{1}{3} \\ =\frac{9}{21}+\frac{105}{21}+\frac{7}{21} \\ =\frac{9+105+7}{21} \\ =\frac{121}{21} \end{gathered}$

STEP 3: Calculate the earnings of each of them

Erin's

$\begin{gathered} \frac{Erin^{\prime}s\text{ ratio}}{Total\text{ ratio}}\cdot Total\text{ winnings} \\ \\ By\text{ substitution,} \\ \frac{\frac{3}{7}}{\frac{121}{21}}\cdot14780=\frac{3}{7}\cdot\frac{21}{121}\cdot14780=\frac{133020}{121}=\:1099.33884\approx\text{ \ }1099.34 \end{gathered}$

Kim's

$\begin{gathered} \frac{5}{\frac{121}{21}}\cdot14780 \\ =5\div\frac{121}{21}\cdot14780=5\cdot\frac{21}{121}\cdot14780=\frac{1551900}{121}=\:12825.61983\approx\text{ \ }12825.62 \end{gathered}$

Megans's

$\begin{gathered} \frac{1}{3}\div\frac{121}{21}\cdot14780 \\ \frac{1}{3}\cdot\frac{21}{121}\cdot14780=\frac{103460}{121}=855.04132\approx\text{\ }855.04 \end{gathered}$

Hence, the earnings are given as:

Erin's: $1099.34

Kim's: $12825.62

Megan's: $855.04