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The image contains a VAT-related problem where the total cost of a small house extension, including VAT (Value Added Tax) at 13.5%, amounts to €27,240. The problem is broken into two parts:

**(a)** How much money will the builder receive (i.e., the cost before VAT)?
**(b)** How much will go to the Revenue Commissioners in tax (i.e., the total VAT)?

### Solution

#### Part (a): Finding the cost before VAT
Let the cost before VAT be \( x \).

The VAT is charged at 13.5%, so the total cost including VAT is:
\[
\text{Total Cost} = x + (13.5\% \text{ of } x) = x + 0.135x = 1.135x
\]

We know the total cost is €27,240:
\[
1.135x = 27,240
\]
Solving for \( x \) (the cost before VAT):
\[
x = \frac{27,240}{1.135} \approx 24,000
\]

So, the cost before VAT is approximately €24,000.

#### Part (b): Finding the VAT amount
The VAT amount is 13.5% of the cost before VAT, which we now know to be €24,000:
\[
\text{VAT} = 0.135 \times 24,000 = 3,240
\]

Thus, the total VAT is €3,240.

### Final Answer:
- **(a)** The builder will receive €24,000.
- **(b)** The Revenue Commissioners will receive €3,240 in tax.

Would you like further clarification or details?

Here are 5 related questions to expand your understanding:
1. How do you calculate VAT if only the total cost is given?
2. What is the formula to calculate the price before VAT for different VAT percentages?
3. How would the solution change if the VAT percentage were different?
4. How can VAT be calculated in reverse from the final price?
5. How is VAT applied differently in other countries or sectors?

**Tip:** When dealing with VAT or taxes, always ensure to convert the percentage into decimal form (e.g., 13.5% = 0.135) to make calculations easier.

A couple get a small extension done on their house. The total cost, including VAT at 13.5%, comes to €27,240.

(a) How much money will the builder receive (i.e., what is the cost before VAT)?
(b) How much will go to the Revenue Commissioners in tax (i.e., what is the total VAT)?

Learn how to calculate the cost before VAT and the total VAT for a house extension where the total cost is €27,240 and the VAT rate is 13.5%. This step-by-step solution covers percentage calculations and basic algebra, suitable for students in Grades 9-12.

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