Question

1. a car travels $162\\ \frac{1}{2}$ miles on 5 gallons of gas. if the car’s fuel efficiency is constant, which equation represents $m$, the number of miles, the car can travel on $g$ gallons of gas?\

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a. $m = \frac{65}{2}g$\
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b. $m = \frac{2}{65}g$\
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c. $m = \frac{1}{5}g$\
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d. $m = 5g$

Explanation:

Step1: Find miles per gallon

First, convert \(162\frac{1}{2}\) to an improper fraction. \(162\frac{1}{2}=\frac{162\times2 + 1}{2}=\frac{325}{2}\). Then, miles per gallon is \(\frac{\frac{325}{2}}{5}=\frac{325}{2}\times\frac{1}{5}=\frac{65}{2}\).

Step2: Form the equation

Since miles \(m\) is miles per gallon times gallons \(g\), the equation is \(m = \frac{65}{2}g\).

Answer:

a. \(m=\frac{65}{2}g\)