Proportional distribution

2020-11-25T13:23:00+02:00

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.

In proportional distribution, the final number is divided in the proportion indicated by the ratio.

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 $]].

17. Proportional Distribution (Dividing in a given ratio)

Proportional distribution

Example 1

Example 2

Exercises