Question #d0038

1 Answer
Jul 18, 2016

Answer:

#$17#

Explanation:

Notice that the problem provides you with the price of gasoline in dollars per liter, #"$/L"#, but that the volume of the gas tank is given to you in gallons, #"gal"#.

To find the price of a a full tank of gasoline, you must use a conversion factor to take you from liters to gallons. More specifically, you must use

#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 gal " ~~ " 3.7854 L")color(white)(a/a)|)))#

Convert the volume of the gas tank first

#14 color(red)(cancel(color(black)("gal"))) * "3.7854 L"/(1color(red)(cancel(color(black)("gal")))) = "52.996 L"#

Now, you know that you must pay #"$0.325"# for every liter of gasoline that you purchase, which means that #"52.996 L"# will cost you

#52.996 color(red)(cancel(color(black)("L gasoline"))) * "$0.325"/(1color(red)(cancel(color(black)("L gasoline")))) = $17.224#

Rounded to two sig figs, the number of sig figs you have for the volume of the gas tank, the answer will be

#"price of a full tank" = color(green)(|bar(ul(color(white)(a/a)color(black)("$17")color(white)(a/a)|)))#