Question 21 (2 marks) The inflation rate over the year from January 2019 to January 2020 was $2 \%$. The cost of a school jumper in January 2020 was $\$ 122$. Calculate the cost of the jumper in January 2019 assuming that the only change in the cost of the jumper was due to inflation.

Step 1 ：The inflation rate over the year from January 2019 to January 2020 was 2%.

Step 2 ：The cost of a school jumper in January 2020 was $122.

Step 3 ：We are asked to calculate the cost of the jumper in January 2019 assuming that the only change in the cost of the jumper was due to inflation.

Step 4 ：The inflation rate is the percentage increase in prices over a year. If the cost of the jumper in January 2020 was $122 and the inflation rate was 2%, then the cost of the jumper in January 2019 would have been less.

Step 5 ：We can calculate this by dividing the cost in 2020 by 1 plus the inflation rate.

Step 6 ：Let's denote the cost in 2020 as \(cost_{2020}\) and the inflation rate as \(inflation_{rate}\). Then, the cost in 2019, denoted as \(cost_{2019}\), can be calculated as follows: \(cost_{2019} = \frac{cost_{2020}}{1 + inflation_{rate}}\)

Step 7 ：Substituting the given values into the formula, we get: \(cost_{2019} = \frac{122}{1 + 0.02} = 119.6078431372549\)

Step 8 ：Final Answer: The cost of the jumper in January 2019 was approximately \(\boxed{119.61}\).