Question

From 1970 to 1990, the consumer price index (CPI) increased from 38.8 to 130.7. If a tube of toothpaste cost $0.77 in 1970 and the price of toothpaste increased at the same rate as the CPI from 1970 to 1990, by approximately how much did the price of a tube of toothpaste increase from 1970 to 1990?

Answer 1

Increase in the price of toothpaste is $1.82

Explanation:

As we know the formula of consumer price index

`C.P.I.=(P_(1) )/(P).100`

Here P1 = Current price of the the product

P = Price of the product in the base year

Now we will plug in the values for year 1970

`38.8=(0.77)/(P).100`---------(1)

Similarly for year 1990

`130.7=(P_(1) )/(P).100`------------(2)

Now we will divide equation 2 from 1.

`(130.7)/(38.8)=(P_(1) )/(0.77)`

`P_(1)=((130.7)(0.77))/(38.8)=2.59`

Therefore price of toothpaste in year 1990 will be = $2.59

Since in 1970 price of toothpaste was = $0.77

So change in price from 1970 to 1990 = 2.59 - 0.77 = 1.82

Increase in the price of a tube of toothpaste will be $1.82