Question

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

Answer 1

Answer:

Step-by-step explanation:

Cost of a Road Trip Jesse's car gets 30 miles per gallon of gas. (a) If Las Vegas is 285 miles away, how many gallons of gas are needed to get there and then home? (b) If gas is $3.09 per gallon, what is the total cost of the gas for the trip.

Answer 2

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

A)

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

B)

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