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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.

If Q is directly proportional to P and Q = 28 when P = 4, express Q in terms of P, find the value of Q when P = 5, and calculate the value of P when Q = 42.

Learn how to solve a direct proportionality problem where Q is directly proportional to P, given that Q = 28 when P = 4. The solution covers finding Q in terms of P, calculating Q when P = 5, and determining P when Q = 42. Suitable for Grades 7-9 students.

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