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A certain telephone company offers two plans, A and B. Under

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A certain telephone company offers two plans, A and B. Under [#permalink]

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New post 30 Jan 2012, 01:19
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A certain telephone company offers two plans, A and B. Under plan A, the company charges a total of $0.60 for the first 7 minutes of each call and $0.06 per minute thereafter. Under plan B, the company charges $0.08 per minute of each call. What is the duration of a call, in minutes, for which the company charges the same amount under plan A and under plan B?

A. 2
B. 9
C. 15
D. 21
E. 30
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Mar 2012, 11:31, edited 4 times in total.
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A certain telephone company offers two plans, A and B. Under plan A, the company charges a total of $0.60 for the first 7 minutes of each call and $0.06 per minute thereafter. Under plan B, the company charges $0.08 per minute of each call. What is the duration of a call, in minutes, for which the company charges the same amount under plan A and under plan B?

A. 2
B. 9
C. 15
D. 21
E. 30

Let the duration, in minutes, for which the company charges the same under plan A and plan B be t minutes.

Then under plan A the cost would be $0.6+0.06(t-7) and under plan B the cost would be $0.08t. We want these amount to be equal: 0.6+0.06(t-7)=0.08t --> 60+6(t-7)=8t --> t=9.

Answer: B.

Hope it's clear.
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Re: A certain telephone company offers two plans, A and B. Under [#permalink]

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New post 30 Jan 2012, 01:55
Thank you very much... I charged 0,6 for each of the first 7 minutes :)
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Re: A certain telephone company offers two plans, A and B. Under [#permalink]

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New post 30 Jan 2012, 02:28
First 7 Minutes cost 0,6 cent regardless how long you pick up the phone (for Plan A). For every minute after it costs 0.06 cent
For each minute you call with Plan B it costs 0,08$

When is Plan A = Plan B
A: 0,6 + 0,06*(t - 7)
B: 0,08*t

--> 0,6 + 0,06*(t - 7) = 0,08*t
t = 9

Answer B
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Re: A certain telephone company offers two plans, A and B. Under [#permalink]

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New post 30 Jan 2012, 07:49
0.08*t = 0.06*(t - 7)+0.6
t=9
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Re: A certain telephone company offers two plans, A and B. Under [#permalink]

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New post 30 Jan 2012, 08:19
I saw this one recently as well, and was also getting the wrong number.

I managed to correct it within the allotted time, and got t=9, B.
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Re: A certain telephone company offers two plans, A and B. Under [#permalink]

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New post 30 Jan 2012, 15:18
why dont we write this equation like this:
number of minutes be X

0.6(7)+0.06(x-7)=0.08(x). whats wrong with this equation.

according to manhattann word translation guide

Ex: pay $10 for the first 2 CDs then $7 per additional CD.
N is number of CDs bought.
10*2+7(n-2)=T.C

what is the difference
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New post 30 Jan 2012, 15:44
TomB wrote:
why dont we write this equation like this:
number of minutes be X

0.6(7)+0.06(x-7)=0.08(x). whats wrong with this equation.

according to manhattann word translation guide

Ex: pay $10 for the first 2 CDs then $7 per additional CD.
N is number of CDs bought.
10*2+7(n-2)=T.C

what is the difference


The red part is wrong because the company charges a total of $0.60 for the first 7 minutes and not $0.60 per each minute of the first 7 minutes.

In your example I guess it's meant that $10 are paid for each of the first 2 CD's.

Hope it's clear.
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Re: A certain telephone company offers two plans, A and B. Under [#permalink]

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New post 30 Jan 2012, 20:44
Thank you very much bunnel. I got it. I need to concentrate more on wording of the problem
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Re: A certain telephone company offers two plans, A and B. Under [#permalink]

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New post 02 Feb 2012, 10:20
+1 B

The equation to solve this question is:

\(0.6 + 0.06(x-7) = 0.08x\)

To make it easy, we can express it in this way:

\(60 + 6(x-7) = 8x\)

\(x = 9\)

ANSWER: B
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New post 21 Mar 2012, 13:20
Duration be x

0.08x = 0.60 + 0.06(x-7)
0.08x = 0.60 + 0.06x - 0.42
0.02x = 0.18

x = 9

Ans: B
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New post 26 Mar 2012, 00:08
I think backsolving here would be a faster method than actually jotting down the equations.
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Re: A certain telephone company offers two plans, A and B. Under [#permalink]

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New post 02 Jun 2013, 12:26
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Let the total duration of the call be x minutes.

Plan A = 0.60 + 0.06(x-7)

Plan B = 0.08x

Since both the amounts charged are equal, 0.60 + 0.06(x-7) = 0.08x

-0.02x = -0.18

Hence x = 9 minutes
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New post 07 Jul 2014, 19:00
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In the first 7 mins:
Plan A cost 0.6
Plan B cost 0.08*7=0.56
0.6-0.56=0.04 <- Plan A cost 0.04 more

After 7 mins:
Plan A cost 0.06 per min
Plan B cost 0.08 per min
0.08-0.06=0.02 <- Plan B will cost 0.02 more per min

To balance the cost between Plan A and B:
0.04=0.02*2

7+2=9 is the answer
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Re: A certain telephone company offers two plans, A and B. Under [#permalink]

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New post 07 Jul 2014, 20:31
Solved by plugging-in the options

For 2 Minutes,
Plan A = 7;
Plan B = 0.16

For 9 Minutes,
Plan A = 0.6 + 2* 0.06 = 0.6 + 0.12 = 0.72
Plan B = 0.08 * 9 = 0.72

Answer = B
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Re: A certain telephone company offers two plans, A and B. Under [#permalink]

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Re: A certain telephone company offers two plans, A and B. Under   [#permalink] 01 Sep 2015, 04:07
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