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In an imaginary economy, consumers buy only sandwiches and magazines. The fixed basket consists of 20 sandwiches and 30 magazines. In 2006, a sandwich cost $4 and a magazine cost $2. In 2007, a sandwich cost $5. The base year is 2006. If the inflation rate in 2007 was 16 percent, then how much did a magazine cost in 2007?

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thuyntd

Answer:

A magazine cost $2.08 in 2007

Explanation:

Let x be the cost of a magazine in 2007

Inflation rate 16% means 2007 CPI is 116

2006 is base year then 2006 CPI is 100

=> [tex]\frac{Cost\:of\:basket\:in\:2007}{Cost\:of\:basket\:in\:base\:year\:2006} = \frac{116}{100}[/tex] (a)

Cost of basket in 2006 = 20*4 + 30*2 = $140

Cost of basket in 2007 = 20*5 + 30*x = 100 + 30x

Plug into (a): (100+30x)/140 = 116/100

=> 100+30x = 162.4

=> x = 62.4/30 = 2.08

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