You drive an average of 450 miles per week in a car that gets 22 miles per gallon. with gasoline priced at $3.50 per gallon on average, approximately how much would you save each year on gas if you instead had a car that got 40 miles per gallon?

First we have to compute how much we spend money each year. 
Compute like this:
[tex] \frac{450}{22}=20.45 [/tex] is the number of gallons consumed each week. 
In one year there is 48 weeks. 
Then [tex]20.45\times48=981.6[/tex] is the number of gallons a year. 
Now compute the price: 
[tex]3.5\times981.6=\$3435,6[/tex]
We do the same process with a car consuming 40 miles per gallon. 
tex] \frac{450}{40}=11.25 [/tex] gallon consumed per week. 
 [tex]11.25\times48=540[/tex]  gallons consumed per year. 
[tex]3.5\times540=\$1890[/tex] is the amount paid each year in gallons. 
So we are saving the following amount:
[tex]\$3435,6-\$1890=\$1545[/tex]