Question

average gasoline prices (per gallon)
if it cost $11 to fill a gas tank in 1990, how much would it have cost to fill the same tank in 2000?

year	price	price as a percentage of 1990 price	price index (1990 = 100)
1970	$0.36	29.3%	29.3
1980	$1.22	99.2%	99.2
1990	$1.23	100.0%	100.0
2000	$1.56	126.8%	126.8
2010	$2.84	230.9%	230.9

it would have cost $\square$ in 2000.
(round to the nearest cent as needed.)

Explanation:

Step1: Identify the price index for 1990 and 2000

The price index for 1990 is 100.0 (from the table, 1990 row, Price Index column), and for 2000 it is 126.8 (2000 row, Price Index column).

Step2: Set up the proportion

Let \( x \) be the cost in 2000. The proportion is based on the price index: \(\frac{\text{Cost in 1990}}{\text{Price Index in 1990}}=\frac{\text{Cost in 2000}}{\text{Price Index in 2000}}\)

Substitute the known values: \(\frac{11}{100.0}=\frac{x}{126.8}\)

Step3: Solve for \( x \)

Cross - multiply: \( 100.0x = 11\times126.8\)

Calculate \( 11\times126.8 = 1394.8\)

Then \( x=\frac{1394.8}{100.0}=13.948\)

Step4: Round to the nearest cent

Rounding 13.948 to the nearest cent gives 13.95.

Answer:

\( \$13.95 \)