[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.

Given Data

  • Cost of the Camping Van (excluding VAT): £23500
  • VAT Rate: 20%
  • Number of Equal Payments: 18
  • Amount of Each Monthly Payment: £940

Finding the ratio of the deposit Emma pays to the total of the 18 equal payments.

First we will find the VAT Amount

The VAT on the camping van is 20% of £23500.

To calculate the VAT:

VAT=20/100×£23500

Calculating the Total Cost

The total cost Emma has to pay (including VAT) is:

Total Cost=£23500+VAT

Calculating the Total of the 18 Equal Payments

Given that Emma makes 18 equal payments of £940 each:

Total of 18 Payments=18×£940

Finding the Deposit Amount

To find the deposit amount, we subtract the total of the 18 payments from the total cost:

Deposit=Total Cost−Total of 18 Payments

Finding the Ratio

Finally, to find the ratio of the deposit Emma pays to the total of the 18 equal payments:

Ratio=Deposit:Total of 18 Payments

We will then simplify this ratio to its simplest form.

Let’s go ahead and calculate these values.

Conclusion

  1. VAT Amount: The VAT on the camping van is £4700.
  2. Total Cost: Emma has to pay, including VAT, which is £28200.
  3. Deposit Amount: Emma pays a deposit of £11280 for the camping van.
  4. Ratio: The ratio of the deposit Emma pays to the total of the 18 equal payments is 2:

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