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Total time is 3 hours 20 mins. Let evaluate total charge for plan A:

Plan A - entry fee + x+ x = 2x + entry fee

Plan B - (3x/2) +(3x/2)+(3x/2)+(3x/2) = 6x

Now , 2x + entry fee = 6x

therefore entry fee = 4x

If we check total charge for plan B option by option , we see that entry fee also needs to be an integer. So only pair satisfying and consistent is

Plan B total charge = $12
Plan A entry fee = $8
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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.
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For 3 hrs and 20 minutes,
A = e + 2x, where e is the one-time entry fee
B = 3x/2 + 3 * (3x/2) = 4 * (3x/2) = 6x

These two are equal
e + 2x = 6x, gives e = 4x

So entry fee : plan b's total = 4x : 6x = 2:3
We test options and can find that 8/12, the entry fee is 8, and plan b's total is 12
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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.
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Entry fee = X
Plan A: X + 2x (1)
Plan B: 3x/2*4 = 6x (2)
(1)(2) => A = B => X+2X = 6X => X = 4x, Plan B: 6x
Looking at options: A = 8, B = 12
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Time = 3h 20min
Plan A = Fee + 2x
Plan B = 3x/2*4 = 6x
Fee + 2x = 6x => Fee = 4x
Scan the options:
Fee = 8 => x = 2 => Plan B = 12

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.
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Given that any fraction of an hour is considered a full hour the total time is thus 4 hours
Plan A total cost is EF+2X
While plan B= 3X/2X4= 6X
We are told total cost is the same so EF+2X=6X
EF=6X-2X=4X
EF=4X
So the ratio of EF for A to total amount for B is the ratio of 4:6 or 8:12 or 12:18
Hence 8 (entry fee for A) and 12 (Total fee for B)
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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.
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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.

Charge is for the full hour, even if a faction of time exceeds a certain hr.

Plan A:

One time entry fee, which is for 2 hours. Plus, $x per hour for every hour exceeding 2 hours.

Plan A = Entry fee + $x * (t-2)

Where t is the total number of hours.

Plan B:

$ (3x/2) for the first hour.

$ (3x/2) for each additional hour.

Plan B = $(3x/2) * t

Given that : Total time = 3 hours and 20 minutes = 4 hrs = t.

Plan A : Entry fee + $ (4-2)*x = Entry fee + $2x

Plan B = $(3x/2)*4 = $6x

Both the values are equal:

Entry fee + $ 2x = $ 6x

Entry fee = $4x

The ratio of Entry fee : Plan B = 4x : 6x

At x = 2, we get entry fee as 8, Plan B = 12

Entry fee = $8

Plan B = $12
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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.

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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.
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Let plan A charge A fixed fees. For 3h 20 min, the charge is A+2x

Under plan B, the charges are 6x.

To make the charges equal, A has to be equal to 4x. The question asks for 4x and 6x or values in the ratio 2:3. If A = 8, then total charge for B is 12 and both are present in the options.

Therefore, Plan A entry fee = 8 and Plan B total charge = 12
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Let entry fee is E for plan A.

Since fraction of an hour is also considered at same rate hence take it as complete hour so E + 2x = 3x/2 + 3* 3x/2 ---> E = 4x
so E/6x = 4x/6x = 2/3

from optoin take both values such as their ration is 2/3.
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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.
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Calculating billable hours:
3 hours 20 minutes = 3.33 hours
Plan A: First 2 hours included => remaining 1.33 hours, charged as 2 hours
Total = Entry fee + 2x

Plan B: First hour + remaining 2.33 hours, charged as 3 hours
=> Total = 4 × (3x/2) = 6x
Setting totals equal
Entry fee+2x=6x
Entry fee=4x

Match values from the table:
Entry fee:
Plan B total = 4x : 6x = 2 : 3

Only pair with ratio 2 : 3 is: 8 and 12
Answer IMO : Plan A entry fee = 8
Plan B total charge = 12
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 ($), that could be Plan A's entry fee and Plan B’s total charge for 3 hours and 20 minutes such that both plans would charge the same total amount. Make only two selections, one in each column.
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Time packed = 3hrs 20 min
Plan A= Entry fee = ? - Covers first 2 hrs
Each Additional hour= X$
Extra hours = 2
cost= Entry fee + 2x
Plan B= no entry fee
charges 3x/2$ per hour or fraction
Total parking is hours 4 hrs
cost per hour = 3x/2 * 4= 6 x

Total = Entry fee + 2x = 6x
Entry fee = 6x-2x=4x
Answer choices: 4,5,8,12,15,20
The only matching pair is 8 & 12 because 8=4x, x=2 ; 12=6x, x=2

Final answer: plan A entry fee is 8
Plan B total is 12
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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.
Total hour = 3 hour 20 minutes or we can say we need to find the charge for 4 hours.

Plan A: Entry fee for 2 hours + x for each additional hour = E+2x

Plan B: (3x/2) for first hour and (3x/2) for each additional hour = (3x/2)*4 = 6x

Plan A charge = Plan B charge
E+2x=6x or E=4x

Plan B total charge= 6x=6(E/4) = 1.5E

Try choice given in the question
If E=4, Then B=1.5*4=6 .....No
If E=5, then B=1.5*5=7.5 .....No
If E=8, then B=1.5*8=12 .....Yes

Plan A Entry fee=8
Plan B total charge=12
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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.


For 3 hours & 20 minutes

Plan A - let's consider charges a as entree fee than total charges will be = a+2x

Plan B - Total charges = 3x/2*4 = 6x

Given 6x=a+2x ----> a=4x

We need to find Plan A entry fee which is 4x, and total charge of plan B which which is 6x....

Taking ratio of 4x/6x = 2/3...Possible pair of answer can be (2,3) (4,6) (6,9) (8,12) (10,15) (20,30)..

Answer (8,12) as the only options given.
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use the equation made from the information - y+2x=3x/2*4, hence y=4x and x is y/4 hence it should be 1.5 times the A charge, hence 8 and 12 are the only options helping here.
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Plan A total charge = Plan A entry fee + 2x
Plan B total charge = 4*3x/2 = 6x
x = (Plan B total charge)/6

Plan A entry fee + 2x = 6x
Plan A entry fee = 4x = 4*(Plan B total charge)/6 = 2*(Plan B total charge)/3

It works choosing:

Plan A entry fee=8 and Plan B total charge=12
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Plan A: entry fee + 2 additional hours = entry fee + 2x
Plan B: 1st hour + 3 additional hours = 3x/2 + 3*3x/2 = 12x/2 = 6x

entry fee + 2x = 6x
entry fee = 4x

Substituting value of x = Plan B/6

entry fee = 2 * Plan B/3
Plan B = 3 * entry fee/2

Plan B=12 and entry fee=8

Plan A entry fee=8
Plan B total charge=12
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Time needed for rent = 3 hours 20 mins

Plan A = entry fees(e) + 2x
Plan B = 4*3x/2 = 6x

For this time both plans have same cost, hence
e + 2x = 6x
=> e = 4x

Plan A entry fees = e = 4x
Plan B total = 6x

Using x = 2 basis options
Plan A entry fees = 8
Plan B total = 12

Bunuel
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12 Days of Christmas Competition
This question is part of our holiday event
Win $40,000 in prizes: courses, tests, and more


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.
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