Question

The cost of a car rental is ​$42 per day plus 20 cents per mile. you are on a daily budget of ​$98. 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.

Answer 1

R= $42 rental cost per day
Mileage= $0.20 per mile
m= number of miles driven
Budget= $98 per day

EQUATION
$98> $0.20m + $42

SOLUTION
$98> $0.20m + $42
subtract 42 from both sides
$56> $0.20m
divide both sides by $0.20
280> m

They have to drive less than 280 miles per day to stay within their $98 budget.

SAME SOLUTION INEQUALITIES
Set up the equations with new numbers, substitute 280 for m and pick another variable to solve for. I chose to solve for total rental cost.

m= 280 miles per day
R= Rental cost per day

R> $0.10(280) + $50
R> $28 + $50
R> $78

Equation #1
$78> $0.10m + $50

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m= 280 miles per day
R= Rental cost per day

R> $0.18(280) + $44
R> $50.40 + $44
R> $94.40

Equation #2
$94.40> $0.18m + $44

ANSWER: 280> m; They have to drive less than 280 miles per day to stay within their $98 budget.

Equation #1: $78> $0.10m + $50
Equation #2: $94.40> $0.18m + $44

Hope this helps! :)