Question

From 1970 to 1980, the consumer price index (CPI) increased from 38.8 to 82.4. If a dozen eggs cost $0.25 in 1970 and the price of eggs increased at the same rate as the CPI from 1970 to 1980, approximately how much did a dozen eggs cost in 1980?

Answer 1

Understanding the Question
This may not be the actual way that the US government prepares the CPI, but it will provide a comparison. 

You can set up a proportion. The base number for the CPI is 38.8 in 1970. That number (38.8) has more than doubled to get to 82.4, which also tells us that there was inflation. What your parents and grandparents bought in 1970 went to double the amount in 1980. Gasoline certainly did that.

Givens
CPI in 1970 = 38.8
CPI in 1980 = 82.4
Eggs 1970 =  0.25
Edgs 1980 = X

Formula substitution and solution
CPI 1970 / CPI 1980 = cost of eggs 1970 / cost of eggs 1980
38.8/82.4 = 0.25 / x Cross multiply
38.8 * x = 0.25 * 82.4
38.8 * x = 20.625
x = 20.628 /38.8
x = 0.53 dollars of 53 cents.

53 cents in 1980 which is slightly double as predicted.

Footnote
As a matter of interest, my wife tells me that eggs now cost about 3.58 where we live. That's almost 7 times as expensive as they were in 1980. Something to think about. By the way, the price quoted is in Canada.