Question

An automobile travels 305 miles on 16 2/3 gallons of gasoline.

A. How many miles per gallon does the car get on the trip? (Enter as a simplified mixed number. )

B. How many gallons would be required for the car to travel 549 miles?

Answer 1

a. The automobile gets 18.3 miles per gallon.

b. To travel 549 miles, it would require approximately 30 gallons of gasoline.

Step-by-step explanation:

A. Calculating Miles Per Gallon

To find out how many miles per gallon the automobile gets, divide the total number of miles traveled by the total gallons of gasoline used.

The equation is:

Miles per gallon = Total miles traveled ÷ Total gallons of gasoline used.

Therefore, we have:

Miles per gallon = 305 miles ÷ 16 2/3 gallons

First, convert 16 2/3 gallons to an improper fraction:

(16 × 3) + 2 = 50/3 gallons.

Now, calculate the miles per gallon: 305 miles ÷ (50/3) gallons = 305 × 3/50 = 18 3/10 or 18.3 miles per gallon (simplified mixed number).

B. Gallons Required for 549 Miles

To determine how many gallons would be required for the car to travel 549 miles, use the miles per gallon calculated in part A.

The equation is:

Gallons required = Total miles to travel ÷ Miles per gallon.

Gallons required = 549 miles ÷ 18.3 miles/gallon = 30 (rounded to the nearest whole number since it is not practical to pump a fraction of a gallon).

Answer 2

let's firstly convert the mixed fraction to improper fraction and then proceed from there.

A)

`\stackrel{mixed}{16(2)/(3)}\implies \cfrac{16\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{50}{3}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{array}{ccll} miles&gallons\\ \cline{1-2} 305&(50)/(3)\\[1em] x&1 \end{array}\implies \cfrac{305}{x}=\cfrac{~~ (50)/(3)~~}{1}\implies \cfrac{305}{x}=\cfrac{50}{3}\implies 915=50x \\\\\\ \cfrac{305}{50}=x\implies \cfrac{183}{10}=x\implies 18(3)/(10)=x`

B)

`\begin{array}{ccll} miles&gallons\\ \cline{1-2} 305&(50)/(3)\\[1em] 549&g \end{array}\implies \cfrac{305}{549}=\cfrac{~~ (50)/(3)~~}{g}\implies \cfrac{305}{549}=\cfrac{~~ (50)/(3)~~}{(g)/(1)}\implies \cfrac{305}{549}=\cfrac{50}{3}\cdot \cfrac{1}{g} \\\\\\ \cfrac{305}{549}=\cfrac{50}{3g}\implies 915g=27450\implies g=\cfrac{27450}{915}\implies g = 30`