QuestionWrite an equation for the linear function and use it to answer the given question. The cost of renting a car is a flat $\$ 28$ , plus an additional 7 cents per mile that you drive. How far can you drive for $\$ 96$ ? A. $r=28+0.07 \mathrm{~m} ; 971$ miles B. $r=28 m+0.07 ; 3$ miles C. $r=28-0.07 \mathrm{~m} ; 1,771$ miles D. $r=28 m-0.07 ; 3$ miles

Studdy Solution

STEP 1

1. The cost of renting a car is a flat $28.<br />2. There is an additional cost of 7 cents per mile driven.<br />3. We need to find how far you can drive for a total cost of$ 96.

STEP 2

1. Define variables and write the linear equation for the cost.
2. Substitute the given total cost into the equation.
3. Solve the equation for the number of miles driven.

STEP 3

Define variables and write the linear equation for the cost.
Let $r$ be the total rental cost in dollars, and $m$ be the number of miles driven.
The cost equation is:
$r = 28 + 0.07m$

STEP 4

Substitute the given total cost into the equation.
Given that the total cost $r = 96$ , substitute into the equation:
$96 = 28 + 0.07m$

STEP 5

Solve the equation for the number of miles driven.
Subtract 28 from both sides to isolate the term with $m$ :
$96 - 28 = 0.07m$ $68 = 0.07m$
Divide both sides by 0.07 to solve for $m$ :
$m = \frac{68}{0.07}$ $m = 971.43$
Since you cannot drive a fraction of a mile, round down to the nearest whole number:
The number of miles you can drive is:
$\boxed{971}$

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