Daniel wants to buy a bike - Junior Cycle Mathematics - Question 3 - 2015

To calculate the special offer price:

1. Calculate 1/4 of the usual price:

   $\frac{1}{4} \ of \ 320 = \frac{320}{4} = 80$

2. Subtract this amount from the usual price:

   $320 - 80 = 240$

Thus, the "special offer" price is €240.

To calculate the total amount Daniel will pay:

1. Calculate the total payments:

   Money paid at the beginning: €60 Money paid at the end of each month for 12 months:

   $20 \times 12 = 240$

2. Thus, total amount paid:

   $60 + 240 = 300$

Thus, the "special offer" price is €300.

Daniel should buy the bike in Shop B because it has the lowest special offer price of €240.

Shop C requires a larger total payment of €300, and while Shop A offers a price of €288, it is still more than Shop B.

To determine the VAT:

1. Let the selling price including VAT be S and the rate of VAT be r (expressed as a decimal).

2. The formula to find the price excluding VAT is:

   $\text{Price excluding VAT} = \frac{S}{1 + r}$

3. The amount of VAT charged is:

   $\text{VAT} = S - \frac{S}{1 + r}$

For example, if the selling price is €55 and the VAT rate is 10% (0.1):

1. Calculate the amount excluding VAT:

   $\frac{55}{1 + 0.1} = \frac{55}{1.1} \approx 50$

2. The VAT amount would then be:

   $55 - 50 = 5$

Hence, €5 is the VAT charged.