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If it cost [tex]$\$3$[/tex] to fill a gas tank in 1970, how much of the same tank could be filled with [tex]$\$3$[/tex] in 2000?

Average Gasoline Prices (per gallon):

[tex]
\[
\begin{array}{|l|c|c|c|}
\hline
\text{Year} & \text{Price} & \begin{array}{c}
\text{Price as a Percentage} \\
\text{of 1980 Price}
\end{array} & \begin{array}{c}
\text{Price Index} \\
(1980=100)
\end{array} \\
\hline
1960 & \$0.31 & 25.4\% & 25.4 \\
1970 & \$0.36 & 29.5\% & 29.5 \\
1980 & \$1.22 & 100.0\% & 100.0 \\
1990 & \$1.23 & 100.8\% & 100.8 \\
2000 & \$1.56 & 127.9\% & 127.9 \\
2010 & \$2.84 & 232.8\% & 232.8 \\
\hline
\end{array}
\]
[/tex]

About [tex]$\square$[/tex] of the same tank could be filled.
(Type an integer or decimal rounded to two decimal places as needed.)

Answer :

To solve this question, let’s calculate how much of the same tank could be filled in the year 2000 with [tex]$3, compared to 1970.

1. Determine the Price Per Gallon for Each Year:
- In 1970, the cost of gasoline was $[/tex]0.36 per gallon.
- In 2000, it was [tex]$1.56 per gallon.

2. Calculate How Many Gallons $[/tex]3 Could Buy in Each Year:
- For 1970: Divide [tex]$3 by the price per gallon in 1970.
\[
\frac{3}{0.36} = 8.33\ \text{gallons}
\]
- For 2000: Divide $[/tex]3 by the price per gallon in 2000.
[tex]\[
\frac{3}{1.56} = 1.92\ \text{gallons}
\][/tex]

3. Determine the Proportion of the Tank Filled:
- Find the ratio of how much of the tank could be filled in 2000 compared to 1970.
[tex]\[
\frac{1.92}{8.33} \approx 0.23
\][/tex]

So, with [tex]$3 in 2000, you could fill about 0.23 (or 23%) of the same tank that you could fill with $[/tex]3 in 1970.

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