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Let's solve this step by step.

Let:
- \( b \) be the cost of a book.
- \( m \) be the cost of a magazine.

The problem states two key pieces of information:
1. The cost of a book is twice that of a magazine: \( b = 2m \).
2. The total cost of 1 book and 4 magazines is £24: \( b + 4m = 24 \).

### Step 1: Substitution
From the first equation, \( b = 2m \). We can substitute this value into the second equation:
\[
2m + 4m = 24
\]
### Step 2: Simplify the equation
\[
6m = 24
\]
### Step 3: Solve for \( m \)
\[
m = \frac{24}{6} = 4
\]
So, the cost of a magazine is £4.

### Step 4: Find the cost of the book
Since \( b = 2m \), substitute \( m = 4 \) into this equation:
\[
b = 2 \times 4 = 8
\]
Thus, the cost of a book is £8.

### Final Answer:
The book costs £8.

Would you like further details on any part of this solution?

Here are 5 related questions for you to explore:
1. What would be the total cost of 3 books and 5 magazines?
2. If the cost of the book increases by 25%, what would be the new price?
3. How many magazines can be bought for the same price as 2 books?
4. If the total budget is £50, how many books and magazines can you buy?
5. How does the solution change if the cost of a book was three times the price of a magazine?

**Tip:** When solving word problems, always define your variables and organize the information before forming equations.

The cost of a book is twice that of a magazine. 1 book and 4 magazines cost £24. How much does a book cost?

Learn how to solve the problem where the cost of a book is twice that of a magazine, and 1 book and 4 magazines cost £24. A step-by-step algebraic solution is provided. Suitable for students in Grades 6-8.

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