Often, costs or profits are distributed in such a way that not everyone involved receives the same amount. If two friends have bought a lottery ticket with one friend paying QAR [[$ 3 $]] and the other paying QAR [[$ 9 $]], it is not fair to split the profit in half. The profit must be distributed in the same proportion as the initial investments are in relation to each other.

Example 1

Divide [[$ 32\: QAR $]]​ by the ratio [[$ 3 : 5 $]]​.

Method I

Use information about how many parts there are in total.

 The other part of the unit to be distributed is [[$ \displaystyle\frac {3} {8} $]]​, whereas the other part is [[$ \displaystyle\frac {5} {8} $]].

[[$ \displaystyle\frac {3} {8} \cdot 32 \:QAR = 12 \:QAR $]]​

[[$ \displaystyle\frac {5} {8} \cdot 32 \:QAR = 20 \: QAR $]]​

When finished, remember to check the answer: [[$ 12 \:QAR + 20 \:QAR = 32 \:QAR $]]​

Method II

Write an equation to find out the answer.

​[[$ \quad \begin{align} 3x + 5x &= 32 \ \\ 8x &= 32 \space ||:8 \ \\ x &= \dfrac{32}{8} \ \\ x &= 4 \end{align} $]]​

Then, calculate the values of the two parts: [[$ 3x = 3 \cdot 4 = 12 $]]​ and [[$ 5x = 5 \cdot 4 = 20 $]]​.

Answer: The parts are [[$ 12 $]]​ QAR and [[$ 20 $]]​ QAR.

Example 2

Divide the number [[$ 348 $]] into three parts relative to [[$ 1: 2: 3 $]].

Method I

There are [[$ 1 + 2 + 3 = 6 $]]​ parts in total.

The first part: [[$ \displaystyle\frac {1} {6} \cdot 348 = 58 $]]

The second part: [[$ \displaystyle\frac {2} {6} \cdot 348 = 116 $]]​

The third part: [[$ \displaystyle\frac {3} {6} \cdot 348 = 174 $]]​

Check your answer: [[$ 58 + 116 + 174 = 348 $]]​

Method II

Write an equation to find out the answer.

[[$ \quad \begin{align} x + 2x + 3x &= 348 \ \\ 6x &= 348 \space ||:6 \ \\ x &= \dfrac{348}{6} \ \\ x &= 58 \end{align} $]]​

Calculate the parts: [[$ x = 58 $]]​ , [[$ 2x = 2 \cdot 58 = 116 $]]​ and [[$ 3x = 3 \cdot 58 = 174 $]]​

Answer: [[$ 58 $]]​, [[$ 116 $]]​ and [[$ 174 $]]​.