# [Solved] Emma buys a camping van for £23500 plus VAT at 20%. She pays a deposit for the camping van. She then pays the rest of the cost in 18 equal payments of £940 each month. Find the ratio of the deposit Emma pays to the total of the 18 equal payments. Give your answer in its simplest form.

**Concept used:**

This question involves several mathematical concepts, including:

- Percentage calculations: In this case, we had to calculate the VAT (Value Added Tax) amount, which was given as a percentage (20%) of the base price of the camping van (£23,500).
- Linear equations: The total cost of the camping van can be represented as the sum of the deposit and the total of the 18 equal payments. This relationship can be expressed as a linear equation: Total cost = Deposit + Total of 18 equal payments.
- Ratios: The problem asks for the ratio of the deposit Emma pays to the total of the 18 equal payments. Ratios are used to compare two or more quantities.
- Simplifying ratios: The ratio found in the problem needs to be simplified to its lowest terms. This involves finding the greatest common divisor (GCD) of the two numbers in the ratio and dividing both numbers by the GCD.

By applying these concepts, we can find the correct simplified ratio of the deposit Emma pays to the total of the 18 equal payments, which is 2:3.

**Emma buys a camping van for £23500 plus VAT at 20%. She pays a deposit for the camping van. She then pays the rest of the cost in 18 equal payments of £940 each month. The ratio of the deposit Emma pays to the total of the 18 equal payments is 2:3.**

**Step-by-step explanation:**

**Step 1: Calculate the VAT**

Value Added Tax (VAT) is a consumption tax added to the price of certain goods and services.

In this problem, the camping van has a VAT of 20%. To find the VAT amount, we calculate 20% of the original price (£23,500):

VAT = (20 / 100) * £23,500 VAT = 0.20 * £23,500 VAT = £4,700

So, the VAT amount for the camping van is £4,700.

**Step 2: Calculate the total cost of the camping van**

The total cost of the camping van includes the original price and the VAT amount.

To find the total cost, we add the VAT (£4,700) to the original price (£23,500):

Total cost = Original price + VAT

Total cost = £23,500 + £4,700 Total cost = £28,200

So, the total cost of the camping van is £28,200.

**Step 3: Calculate the total of the 18 equal payments**

Emma is paying the rest of the cost of the camping van in 18 equal monthly payments of £940 each.

To find the total amount paid through these instalments, we multiply the number of payments (18) by the amount of each payment (£940):

Total of 18 equal payments = Number of payments * Amount of each payment

Total of 18 equal payments = 18 * £940

Total of 18 equal payments = £16,920

So, the total amount Emma pays through the 18 equal payments is £16,920.

**Step 4: Calculate the deposit paid by Emma**

To find the deposit Emma paid, we need to subtract the total amount of the 18 equal payments (£16,920) from the total cost of the camping van (£28,200):

Deposit = Total cost – Total of 18 equal payments

Deposit = £28,200 – £16,920 Deposit = £11,280

So, Emma pays a deposit of £11,280.

**Step 5: Find the ratio of the deposit to the total of the 18 equal payments**

Now, we need to find the ratio of the deposit Emma paid (£11,280) to the total amount of the 18 equal payments (£16,920).

We start by writing the ratio as:

Ratio = Deposit : Total of 18 equal payments Ratio = £11,280 : £16,920

We find both numbers’ greatest common divisor (GCD) to simplify the ratio.

The GCD of £11,280 and £16,920 is £2,640.

Now, divide both numbers by their GCD:

£11,280 / £2,640 = 4 £16,920 / £2,640 = 6

The simplified ratio is:

Ratio = 4:6

This ratio can be further simplified by dividing both numbers by their GCD, which is 2:

4 / 2 = 2 6 / 2 = 3

Therefore, the simplest form of the ratio is:

Ratio = 2:3

**So, the ratio of the deposit Emma pays to the total of the 18 equal payments is 2:3**