Question

If 42 notebooks were distributed among 6 children, among how many children would 28 notebooks have to be distributed if each had to get the same number of notebooks as before?

Answer 1

42 notebooks are distributed among 6 children.
Let 28 notebooks be distributed among x children.
The given information can be represented in the following table:

Number of children : x	6	x
Number of notebooks : y	42	28

Here, distribution of number of notebooks and number of children are in direct proportion because number of children will decrease with a decrease in the number of notebooks. In direct variation, the ratio of the number of children to the number of notebooks must be constant, i.e
$$\begin{gathered} \frac{x_1}{y_1}=\frac{x_2}{y_2} \\ \therefore \frac{6}{42}=\frac{x}{28} \\ x=\frac{6}{42}\times 28=4 \end{gathered}$$

Thus, 28 notebooks will have to be distributed among 4 children.