Direct/Inverse Proportion Textbook Exercise - Corbettmaths - Free Printable

Let's solve Question 1 in detail, as it's the first one fully visible and a good example of direct proportion. We'll go through each part step by step.

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Question 1:

A is directly proportional to B.
When $ A = 12 $, $ B = 3 $

#### (a) Find a formula for A in terms of B

When two quantities are directly proportional, we write:
$$
A \propto B
$$
This means:
$$
A = k \cdot B
$$
where $ k $ is the constant of proportionality.

We are given that when $ A = 12 $, $ B = 3 $. Plug these into the equation to find $ k $:

$$
12 = k \cdot 3
$$

Solve for $ k $:
$$
k = \frac{12}{3} = 4
$$

So the formula is:
$$
\boxed{A = 4B}
$$

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#### (b) Find the value of A when B = 5

Use the formula $ A = 4B $:
$$
A = 4 \times 5 = 20
$$

Answer: $ \boxed{A = 20} $

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#### (c) Find the value of B when A = 36

Use $ A = 4B $, substitute $ A = 36 $:
$$
36 = 4B
$$

Solve for $ B $:
$$
B = \frac{36}{4} = 9
$$

Answer: $ \boxed{B = 9} $

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✔ Final Answers for Question 1:

- (a) $ A = 4B $
- (b) $ A = 20 $
- (c) $ B = 9 $

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Now let’s do Question 2 using the same method.

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Question 2:

C is directly proportional to D.
When $ C = 125 $, $ D = 5 $

#### (a) Find an equation for C in terms of D

Since $ C \propto D $, then:
$$
C = kD
$$

Substitute $ C = 125 $, $ D = 5 $:
$$
125 = k \cdot 5 \Rightarrow k = \frac{125}{5} = 25
$$

So:
$$
\boxed{C = 25D}
$$

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#### (b) Find the value of C when D = 10

$$
C = 25 \times 10 = 250
$$

Answer: $ \boxed{C = 250} $

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#### (c) Find the value of D when C = 75

Use $ C = 25D $:
$$
75 = 25D \Rightarrow D = \frac{75}{25} = 3
$$

Answer: $ \boxed{D = 3} $

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✔ Final Answers for Question 2:

- (a) $ C = 25D $
- (b) $ C = 250 $
- (c) $ D = 3 $

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Question 3:

E is directly proportional to F.
When $ E = 2 $, $ F = 8 $

#### (a) Find an equation for E in terms of F

$ E \propto F \Rightarrow E = kF $

Substitute values:
$$
2 = k \cdot 8 \Rightarrow k = \frac{2}{8} = \frac{1}{4}
$$

So:
$$
\boxed{E = \frac{1}{4}F}
$$

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#### (b) Find the value of E when F = 30

$$
E = \frac{1}{4} \times 30 = 7.5
$$

Answer: $ \boxed{E = 7.5} $

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#### (c) Find the value of F when E = 100

$$
100 = \frac{1}{4}F \Rightarrow F = 100 \times 4 = 400
$$

Answer: $ \boxed{F = 400} $

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✔ Final Answers for Question 3:

- (a) $ E = \frac{1}{4}F $
- (b) $ E = 7.5 $
- (c) $ F = 400 $

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Question 4:

y is directly proportional to x.
When $ x = 400 $, $ y = 10 $

#### (a) Find a formula for y in terms of x

$ y \propto x \Rightarrow y = kx $

$$
10 = k \cdot 400 \Rightarrow k = \frac{10}{400} = \frac{1}{40}
$$

So:
$$
\boxed{y = \frac{1}{40}x}
$$

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#### (b) Find the value of y when x = 200

$$
y = \frac{1}{40} \times 200 = 5
$$

Answer: $ \boxed{y = 5} $

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#### (c) Find the value of x when y = 15

$$
15 = \frac{1}{40}x \Rightarrow x = 15 \times 40 = 600
$$

Answer: $ \boxed{x = 600} $

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✔ Final Answers for Question 4:

- (a) $ y = \frac{1}{40}x $
- (b) $ y = 5 $
- (c) $ x = 600 $

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🔍 Summary of Method:

For direct proportion problems:
1. Write $ A = kB $
2. Use given values to find $ k $
3. Use the formula to answer other parts

This works because if $ A \propto B $, then $ A/B = k $ (constant).

Let me know if you'd like help with inverse proportion next!