Answer: You can drive, at most, 2.95 miles per day.
x ≤ 2.95
Step-by-step explanation:
In a single day, you can spend at most $90
Then if C represents the cost of renting the car, then we will have the inequality:
C ≤ $90
Now let's find the equation for C.
We know that we have a fixed cost of $25 plus $22 per mile, then if you drive x miles, the total cost will be $25 plus x times $22, or:
C = $25 + x*$22.
We can now replace that in the inequality:
$25 + x*$22 ≤ $90
Now let's isolate the variable x
x*$22 ≤ $90 - $25
x*$22 ≤ $65
x ≤ $65/$22 = 2.95
x ≤ 2.95
You can drive at most, 2.95 miles per day.
To find other inequalities with the same solution we can start with the solution:
x ≤ 2.95
Now let's multiply both sides by a number (the units of the number can be dollars, in that way we can make a similar problem)
Let's multiply both sides by $10:
x*$10 ≤ 2.95*$10 = $29.5
x*$10 ≤ $29.5
Now let's add the same number in both sides, for example, $5.
x*$10 + $5 ≤ $29.5 + $5 = $34.5
x*$10 + $5 ≤ $34.5
We could write this problem as:
"To rent a cab in your city, you have an initial cost of $5, plus $10 for each mile driven. How many miles could you drive if at most you can spend $34.50?"
You could be more creative with the problem, but this is the way in which you can craft problems of this type when you already know the solution.
