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13 Jan 2026, 12:58
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Plan A entry fee: 8
Plan B total charge: 12
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 $\(\frac{3x}{2}\) for the first hour and $\(\frac{3x}{2}\) 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.
• 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 $\(\frac{3x}{2}\) for the first hour and $\(\frac{3x}{2}\) 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.
| Plan A entry fee | Plan B total charge | |
| 4 | ||
| 5 | ||
| 8 | ||
| 12 | ||
| 15 | ||
| 20 |
ShowHide Answer
Official Answer
Plan A entry fee: 8
Plan B total charge: 12
13 Jan 2026, 12:58
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Bookmarks
Official Solution:
Plan A:
The entry fee covers the first 2 hours. Time beyond 2 hours is 1 hour 20 minutes, which is billed as 2 additional hours.
So Plan A total = \(F + 2x\), where \(F\) is the entry fee.
Plan B:
For 3 hours 20 minutes, billing “per hour or fraction of an hour” means 4 billed hours total.
So Plan B total = \(4 * \frac{3x}{2} = 6x\).
Set totals equal:
\(F + 2x = 6x\)
\(F = 4x\)
Then Plan B total = \(6x = 1.5F\).
From the options, the only pair where the second is 1.5 times the first is:
\(F = 8\) and Plan B total = \(6x = 1.5F = 12\).
Correct answer:
Plan A entry fee "8"
Plan B total charge "12"
Bunuel
Plan A:
The entry fee covers the first 2 hours. Time beyond 2 hours is 1 hour 20 minutes, which is billed as 2 additional hours.
So Plan A total = \(F + 2x\), where \(F\) is the entry fee.
Plan B:
For 3 hours 20 minutes, billing “per hour or fraction of an hour” means 4 billed hours total.
So Plan B total = \(4 * \frac{3x}{2} = 6x\).
Set totals equal:
\(F + 2x = 6x\)
\(F = 4x\)
Then Plan B total = \(6x = 1.5F\).
From the options, the only pair where the second is 1.5 times the first is:
\(F = 8\) and Plan B total = \(6x = 1.5F = 12\).
Correct answer:
Plan A entry fee "8"
Plan B total charge "12"
