Question

the cost of a car rental is $40 per day plus 19¢ per mile. you are on a daily budget of $59. write and solve an inequality to find the greatest distance you can drive each day while staying within your budget. use pencil and paper. find 2 other two - step inequalities with the same solutions. you can drive at most (square) miles per day.

Explanation:

Step1: Define variables and inequality

Let $m$ = number of miles. Total cost: $40 + 0.19m \leq 59$

Step2: Subtract 40 from both sides

$40 + 0.19m - 40 \leq 59 - 40$
$0.19m \leq 19$

Step3: Divide by 0.19 to solve for m

$\frac{0.19m}{0.19} \leq \frac{19}{0.19}$
$m \leq 100$

First equivalent inequality:

Step1: Multiply original by 100

$100(40 + 0.19m) \leq 100(59)$
$4000 + 19m \leq 5900$

Step2: Subtract 4000 from both sides

$19m \leq 1900$

Step3: Divide by 19

$m \leq 100$

Second equivalent inequality:

Step1: Rewrite budget as difference

$0.19m \leq 59 - 40$
$0.19m \leq 19$

Step2: Rearrange terms

$19m \leq 1900$

Step3: Solve for m

$m \leq 100$

Answer:

You can drive at most 100 miles per day.
Equivalent inequalities:

1. $4000 + 19m \leq 5900$ (solution: $m \leq 100$)
2. $0.19m \leq 19$ (solution: $m \leq 100$)