2. Methods to solve compound variation

The methods to solve the problems for compound variation are:

 

1. Proportion method:

 

In this method, from the given data, determine whether they are in direct or inverse proportion. Then, the value of the unknown(\(x\)) can be determined using:

  

2. Multiplicative factor method:

 

Let us consider the table to understand how to solve the problem using the multiplicative factor method.

 

 

Here, the unknown quantity is \(x\).

 

Step 1: Compare the unknown value (Quantity \(1\)) with the known values (Quantity \(2\) and Quantity \(3\)).

 

Step 2: If Quantity \(1\) and Quantity \(2\) are in direct variation, then take the multiplying factor as \(\frac{d}{b}\)(take the reciprocal).

 

Step 3: If Quantity \(1\) and Quantity \(3\) are in inverse variation, then take the multiplying factor as \(\frac{c}{e}\)(no change).

 

Step 4: The value of the unknown \(x\) can be determined using \(x = a \times \frac{d}{b} \times \frac{c}{e}\).

 

 

3. Formula method:

 

From the given data, identify Persons(\(P\)), Days(\(D\)), Hours(\(H\)) and Work(\(W\)) and use the formula:

Here, the suffix \(1\) denotes the values from statement \(1\), whereas the suffix \(2\) denotes the values from statement \(2\).