Question

Kimberly goes on a road trip; her car gets 25 miles per gallon (mpg) and gas costs $3.24 per gallon. Let n represent the number of miles Kimberly has traveled since she started driving.
a. Suppose Kimberly has traveled 252 miles (n 252) since she started driving. i. How many gallons of gasoline has she used since she started driving? gallons Preview i. What is the cost of the gasoline that she has used since she started driving?
b. Write an expression in terms of n that represents the number of gallons of gasoline she has used since she started driving.
c. Write an expression in terms of n that represents the cost of the gasoline that she has used since she started driving.

Answer 1

Answer:

a) 10.08 gallons and $32.66 of gas

b) gallons used = n/25

c)cost of the gasoline = $\frac{n}{25}(3.24)$

Step-by-step explanation:

a) We know that Kimberly has traveled 252 miles and we also know that her car gets 25 miles per gallon. We can apply proportions and rule of three:

25 miles ------ 1 gallon

252 miles ----- x gallons

Solving for x:

x gallons = 252 miles(1 gallon)/25 miles= 10.08 gallons.

Thus, she has used 10.08 gallons since she started driving.

Now we need to know the cost of the gasoline that she has used.

We know that each gallon of gas costs $3.24 and she has used 10.08 gallons. Again, we can apply proportions and rule of three:

1 gallon ------ 3.24 dollars

10.08 gallons---- x dollars.

Solving for x we get:

$x=(10.08)(3.24)$= 32.659=32.66 dollars.

Thus, she has used $32.66 of gas since she started driving.

b) Write an expression in terms of n that represents the number of gallons of gasoline she has used since she started driving.

If we know that n is the number of miles that she drives, from what we wrote above, an expression to know the number of gallons she has used would be:

Gallons used = n/25 (since her car gets 25 miles per gallon) where n is the number of miles.

c) Write an expression in terms of n that represents the cost of the gasoline that she has used since she started driving.

Again, to know the cost of the gasoline we first need to know how many gallons she has used. From b) we know that the expression to know how many gallons she has used is n/25. Since each gallon costs $3.24 we will multiply this number by n/25 and we will get the cost (like we did in a))

Therefore, the cost of the gasoline = $\frac{n}{25}(3.24)$ where n is the number of miles.