Okay, cool, the goal here is to smartly make the calculations as simple for us as possible.
For starters, we list the two pricing plans for evening parking in a garage.
Plan A: This has an undefined entry fee or a fixed amount accounting for hours 1 and 2. Then, another undefined hourly rate, which now we can call $x, is levied for each hour - and if a car's parked for a fraction of an hour, that fraction will incur the same $x cost (not adjusted to minutes, essentially).
Plan B: This has no entry fee, but an hourly rate of parking the car that is 1.5 times the hourly rate of Plan A, or $1.5x / hour.
We need to find values of Plan A's entry fee and Plan B's total charge in dollars, such that, when these two values are taken in tandem, we can coherently arrive at a pricing that would be the same for both plans. This will be for 3 hours 20 minutes - which, given the statements above,
will be taken as 4 hours (as the 20 minutes = same cost as an hour).Now, we know Plan A has an undefined entry fee accounting for hours 1 and 2. Now, hours 3 and 4, the next two hours, will be charged at a total of $2x ($x*2).
Now, Plan B will charge $1.5x for all 4 hours - as there is no fixed charge at the beginning. Hence, the total cost altogether is $1.5x*4 = $6x for plan B.
Now, for both Plan A and Plan B to cost the same for the required duration, the cost for both will need to be $6x (or the cost of Plan B). In Plan A, $2x is levied through the hourly rate; hence the remainder -
$4x, will need to be fixed rate for the first two hours. With this, we're simply looking at 4x : 6x or a 2:3 ratio between Plan A entry fee, and Plan B total cost. Among the options, the only ones that make that happen are $8 = Plan A entry fee; and $12 = Plan B total charge.Bunuel
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A driver is choosing between two pricing plans for evening parking in a downtown garage.
• Plan A charges a one time entry fee that covers the first 2 hours, plus $x for each additional hour or fraction of an hour beyond the first 2 hours.
• Plan B charges no entry fee, but charges $3x/2 for the first hour and $3x/2 for each additional hour or fraction of an hour beyond the first hour.
Select for
Plan A entry fee and for
Plan B total charge the two figures, in US dollars ($), that could be Plan A's entry fee and Plan B’s total charge for 3 hours and 20 minutes such that both plans would charge the same total amount. Make only two selections, one in each column.