Let's solve the problem step by step.

Problem:

We are given that $Q$ is directly proportional to $P$, and $Q = 28$ when $P = 4$.

When two variables are directly proportional, we can express this relationship as: $Q = kP$ where $k$ is the constant of proportionality.

(i) Express $Q$ in terms of $P$:

From the given, we know $Q = 28$ when $P = 4$. We can use this to find $k$.

$28 = k \times 4$ Solving for $k$: $k = \frac{28}{4} = 7$

Thus, the equation expressing $Q$ in terms of $P$ is: $Q = 7P$

(ii) Find the value of $Q$ when $P = 5$:

Using the equation $Q = 7P$, substitute $P = 5$: $Q = 7 \times 5 = 35$

Thus, $Q = 35$ when $P = 5$.

(iii) Calculate the value of $P$ when $Q = 42$:

Using the same equation $Q = 7P$, substitute $Q = 42$ and solve for $P$: $42 = 7P$ $P = \frac{42}{7} = 6$

Thus, $P = 6$ when $Q = 42$.

Summary:

(i) $Q = 7P$
(ii) $Q = 35$ when $P = 5$
(iii) $P = 6$ when $Q = 42$

Do you want any further clarifications or detailed explanations?

Here are 5 related questions:

1. What does it mean for two variables to be directly proportional?
2. How would the formula change if $Q$ were inversely proportional to $P$?
3. If $P = 10$, what would be the value of $Q$ based on the relationship?
4. How can you find the constant of proportionality if given a different pair of $Q$ and $P$?
5. Can direct proportionality be represented graphically? If so, what would the graph look like?

Tip: Direct proportionality means that as one variable increases, the other increases at a constant rate. The graph of two directly proportional variables is always a straight line passing through the origin.