Question

When the cpi is 185, an electric razor cost $57.81. what is the difference between the price of an electric razor in 1983 and the cost of an electric razor when the cpi is 207, to the nearest cent? a. $33.44 b. $31.25 c. $26.56 d. $6.88

Answer 1

The difference between the price of an electric razor in 1983 and the cost of an electric razor when the cpi is 207, to the nearest cent is given by: Option D: $6.88

What is consumer price index?

The consumer price index is the new cost of market basket in terms of percentage of old cost of market basket.

• $CPI_t$ = consumer price index in current period
• $C_t$ = cost of market basket in current period
• $C_0$  = cost of market basket in base period

Then, we have:

$CPI_t = \dfrac{C_t}{C_0} \times 100$

For this case, we're given that:

• In 1983, CPI of considered razor = 185, and price = $57.81
• In some other year, the CPI of considered razor = 207, and price = $ ?? (to find).

Let the base price of the razor in some base period be $C_0$  

Then, for year 1983, we get:
$CPI_t = \dfrac{C_t}{C_0} \times 100\\\\185= \dfrac{57.81}{C_0} \times 100\\\\C_0 \approx 31.248 \: \text{(in dollars)}$

Now for the year when CPI is 207, let the price of th razor be $x, then we get:

$CPI_t = \dfrac{C_t}{C_0} \times 100\\\\207 \approx \dfrac{x}{31.248} \times 100\\\\x \approx 64.683 \: \text{(in dollars)}$

The difference between the two prices is:

$d \approx 64.683 - 57.81 = 6.87 \approx 6.88\: \text{(in dollars)}$

Thus, the difference between the price of an electric razor in 1983 and the cost of an electric razor when the cpi is 207, to the nearest cent is given by: Option D: $6.88

Learn more about consumer price index here:

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