Question

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

Answer 1

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=(3)/(7) \\ \\ Kim=5 \\ \\ Megan=(1)/(3) \end{gathered}`

STEP 2: Add the ratios

`\begin{gathered} (3)/(7)+5+(1)/(3) \\ =(3)/(7)+(5)/(1)+(1)/(3) \\ =(9)/(21)+(105)/(21)+(7)/(21) \\ =(9+105+7)/(21) \\ =(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,} \\ ((3)/(7))/((121)/(21))\cdot14780=(3)/(7)\cdot(21)/(121)\cdot14780=(133020)/(121)=\:1099.33884\approx\text{ \$}1099.34 \end{gathered}`

Kim's

`\begin{gathered} (5)/((121)/(21))\cdot14780 \\ =5/(121)/(21)\cdot14780=5\cdot(21)/(121)\cdot14780=(1551900)/(121)=\:12825.61983\approx\text{ \$}12825.62 \end{gathered}`

Megans's

`\begin{gathered} (1)/(3)/(121)/(21)\cdot14780 \\ (1)/(3)\cdot(21)/(121)\cdot14780=(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