Question

2. Problems and Applications Q2 The residents of Vegopia spend all of their income on cauliflower, broccoli, and carrots. In 2016, they spend a total of $210 for 100 heads of cauliflower, $70 for 50 bunches of broccoli, and $45 for 450 carrots. In 2017, they spend a total of $225 for 90 heads of cauliflower, $112 for 80 bunches of broccoli, and $120 for 400 carrots. Complete the following table by calculating the price of one unit of each vegetable in each year. Broccoli Carrots Year 2016 2017 Cauliflower $ $ Using 2016 as the base year, the CPI for 2016 is , and the CPI for 2017 is . The inflation rate in 2017 is % using the CPI. Grade It Now Save & Continue Continue without saving

Answer 1

Find the price of one unit of each vegetable. In 2016, One-unit price of Cauliflower = total spending quantity = 210/100 = $2.1 One-unit price of broccoli = total spending quantity = 70/50 = $1.4 One-unit price of carrot = total spending quantity = 45/450 = $0.1 In 2017, One-unit price of Cauliflower = total spending quantity = 225/90 = $2.5 One-unit price of broccoli = total spending quantity = 112/80 = $1.4 One-unit price of carrot = total spending quantity = 120/400 = $0.3 The required table is as follow: Cauliflower (5) Broccoli (S) Carrots (5) 45/450 = 0.10 2016 210/100 = 2.1 70/50 = 1.4 2017 225/90 = 2.5 112/80 = 1.4 120/400 = 0.3 In base year, CPI is 100 Here, it is given that 2016 is the base year, CPI for 2016 is 100 Find CPI in 2017

Find CPI in 2017 (base quantity of good cauliflower x current price of good cauliflower) + (base quantity of good broccoli x curent price of good broccoli) +(base quantity of good carots x current price of good cauliflower) CPI = - X100 (base quantity of good cauliflower x base price of good cauliflower) + (base quantity of good broccoli x base price of good broccoli) +(base quantity of good carrots x base price of good cauliflower) (100 x $2.5) +(50 $1.4)+(450 $0.3) x100 (100 x $2.1) +(50 Ⓡ$1.4)+(450 x $0.1) 250+ 70+135 210+70+45 = 453x100 = 140 -X100 325 Thus, CPI in 2017 is 140 The following formula is used to calculate rate of inflation percentage change in CPI/prices. ous year(2016) x100 : : CPI in current year(2017)- CPI in pervious year 2016) CPI in pervious year(2016) _140-100 100 = 40% -x100 Thus, inflation rate is 40%