Proportional distribution

Statement

Three partners $A, B, C$ invest in a company $10\,000$, $15\,000$ and $25\,000$ EUR respectively. At the end of the year the total profit is $30\,000$ EUR, to be shared in proportion to the capital contributed. How much does each receive?

Solution

Unknown. $k=$ profit per EUR contributed ($k$ is the annual ROI, “return on investment”).

Equation. The total capital is $50\,000$: $k\cdot 50\,000 = 30\,000 \implies k = 0{,}6$ Therefore: $A$ receives $\;0{,}6\cdot 10\,000=\boxed{6000}$, $B$ receives $\;\boxed{9000}$, $C$ receives $\;\boxed{15000}$. Check: $6+9+15=30$ (thousands of EUR).

Connections

Topics: First-degree equations
Concepts: Equation · Proportionality
Methods: Distribution problem
Skills: Modelling · Solving equations
Exercise type: Word problem