Using Inequalities
A car rents for $23.95/day, plus $.10/mi. Daily budget is $76. What mileage must you stay to remain within budget?
well I set it up as x+.10<76
which doesn't seem right. I am slightly confused on how I'm supposed to set up this equation.
520.5 miles
the equation should look something like this
23.95 + .1x= 76
The phrase "$23.95/day" means you pay $23.95 for every day, or the number of days is multiplied by the amount. So, this becomes 23.95(# days).
Likewise, the phrase "$.10/mi." means you pay $.10 every mile. So, you would multiply the number of miles by $.10.
This becomes .10(# miles)
The equation states you have a "daily budget," so you are talking about only 1 day. You are asked to find the mileage, so that must be the "x."
So your expression is
23.95(1) + .10x
Since you need it under $76, you are correct that the end of the inequality is <76.
The entire inequality becomes:
23.95(1) + .10x <76
simplified, it is
23.95 + .10x <76
Thank You So Much
To set up the equation correctly, you'll need to consider the rental cost per day and the cost per mile driven. Let's break it down step by step:
1. Let's assume that the number of miles driven in a day is represented by the variable "m."
2. The cost of renting the car per day is given as $23.95. This will be a fixed cost regardless of the mileage driven.
3. The additional cost per mile is $0.10. So, for every mile driven, you will incur an extra $0.10 cost.
4. Now we can set up the inequality to represent the daily budget constraint. The total cost for one day is the sum of the fixed daily rental cost and the variable cost based on the miles driven:
Total cost = rental cost + (cost per mile) x (number of miles driven)
Total cost = $23.95 + $0.10m
5. The problem states that the daily budget is $76. So, the inequality to represent this would be:
$23.95 + $0.10m ≤ $76
Now, you can solve this inequality for "m" to find the maximum mileage that will keep you within budget.