Loading...
When Joni, Katrina, and Leah started their business, JKL Enterprises, each contributed an amount of money, in euros. The amounts were in the ratio of \(3:5:8\), respectively, and the first-year profit of JKL Enterprises was split in the same ratio. Katrina's share of the first-year profit was €5,000.
Select for First-year profit and for Leah's share amounts in euros that are consistent with the given information and could be the first-year profit of JKL Enterprises and Leah's share of those profits, respectively. Make only two selections, one in each column.
First year profit
Leah's share
€7,000
€8,000
€9,000
€14,000
€16,000
€18,000
Let's create a simple ratio diagram to show the profit sharing:
Total Profit Split (3:5:8 ratio)
|---Joni---|---Katrina---|-------Leah-------|
3 parts 5 parts 8 parts
= €5,000 = ?
Total parts = \(3 + 5 + 8 = 16\) parts
Since Katrina gets 5 parts out of 16 total parts:
This gives us the key equation:
\(\frac{5}{16} \times \text{Total Profit} = €5,000\)
From our equation: \(\frac{5}{16} \times \text{Total Profit} = €5,000\)
Solving for Total Profit:
Total Profit = \(€5,000 \times \frac{16}{5} = €5,000 \times 3.2 = €16,000\)
Leah gets 8 parts out of 16 total parts:
Leah's share = \(\frac{8}{16} \times €16,000 = \frac{1}{2} \times €16,000 = €8,000\)
Let's check our answer:
Final Answer:
Our answer satisfies all requirements: Katrina receives exactly €5,000 (which is \(\frac{5}{16}\) of €16,000), and the total splits perfectly in the \(3:5:8\) ratio.