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01 Jun 2026, 01:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
78% (02:01) correct
22%
(02:14)
wrong
based on 49
sessions
History
Date
Time
Result
Not Attempted Yet
| Fee | Plan A | Plan B |
| Line 1, Activation Fee | $0 | $50 |
| Line 2, Activation Fee | $0 | $30 |
| Line 1, Monthly Fee | $40 | $35 |
| Line 2, Monthly Fee | $15 | $10 |
The table above shows all applicable charges for 2 phone lines, Line 1 and Line 2, under 2 plans, Plan A and Plan B. Both plans require a monthly fee per phone line, and Plan B requires an additional one-time Line Activation Fee. If n is the number of months for which the total charges for 2 lines under Plan A are equal to the total charges for 2 lines under Plan B, what is n?
A. 4
B. 5
C. 8
D. 10
E. 16
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01 Jun 2026, 01:11
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Official Explanation
For each of the plans, the total charges for n months under that plan is the sum of the two activation fees for that plan added to n times the sum of the two monthly fees for that plan.
Each plan's total charges: (sum of activation fees) + n(sum of monthly fees)
Plan A total charges: (0 + 0) + n(40 + 15) = 55n
Plan B total charges: (50 + 30) + n(35 + 10) = 80 + 45n
The two plans will have the same total charges when 55n = 80 + 45n.
55n = 80 + 45n equation to solve
10n = 80 subtract 45n from both sides
n = 8 divide both sides by 10
Therefore, for 8 months the total charges for 2 lines under Plan A is equal to the total charges for 2 lines under Plan B.
For each of the plans, the total charges for n months under that plan is the sum of the two activation fees for that plan added to n times the sum of the two monthly fees for that plan.
Each plan's total charges: (sum of activation fees) + n(sum of monthly fees)
Plan A total charges: (0 + 0) + n(40 + 15) = 55n
Plan B total charges: (50 + 30) + n(35 + 10) = 80 + 45n
The two plans will have the same total charges when 55n = 80 + 45n.
55n = 80 + 45n equation to solve
10n = 80 subtract 45n from both sides
n = 8 divide both sides by 10
Therefore, for 8 months the total charges for 2 lines under Plan A is equal to the total charges for 2 lines under Plan B.
gchandana
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