a) An item priced at [tex]$P$[/tex] in 2021 had its price raised by [tex]20\%[/tex] in 2022. This year (2023), the price is [tex]10\%[/tex] more than last year. What is the price of the item this year?



Answer :

Certainly! Let's go through the problem step-by-step.

Initially, the price of the shift was [tex]$2000 in the year 2021. 1. Price Increase in 2022: The price increased by 20% in 2022. To calculate the new price for 2022, we need to add 20% of the initial price to the initial price itself. To find 20% of the initial price: \[ 20\% \text{ of } 2000 = 0.20 \times 2000 = 400 \] Therefore, the price in 2022 is: \[ 2000 + 400 = 2400 \] 2. Price Increase in 2023: The price increased by 10% in 2023 from the 2022 price. Again, we need to add 10% of the 2022 price to the 2022 price itself. To find 10% of the 2022 price: \[ 10\% \text{ of } 2400 = 0.10 \times 2400 = 240 \] Therefore, the price in 2023 is: \[ 2400 + 240 = 2640 \] So, the price of the shift in the year 2023 is \( \$[/tex]2640 \).