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The price of a phone call consists of a standard connection

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The price of a phone call consists of a standard connection [#permalink] New post 25 Jul 2018, 17:20
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Question Stats:

93% (01:46) correct 6% (02:41) wrong based on 33 sessions
The price of a phone call consists of a standard connection fee, which is constant, plus a per minute charge. A 10-minute call costs $2.90 and a 16-minute call costs $4.40. How much does a 13-minute call cost?

(A) $3.55
(B) $3.57
(C) $3.58
(D) $3.65
(E) $3.77
[Reveal] Spoiler: OA

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Re: The price of a phone call consists of a standard connection [#permalink] New post 25 Jul 2018, 23:08
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sandy wrote:
The price of a phone call consists of a standard connection fee, which is constant, plus a per minute charge. A 10-minute call costs $2.90 and a 16-minute call costs $4.40. How much does a 13-minute call cost?

(A) $3.55
(B) $3.57
(C) $3.58
(D) $3.65
(E) $3.77



Note: In both cases Standard connection fee is a constant. So any any changes made it's due to call rate.

Now, 2.9 is for 10 mins

4.40 is for 16 mins

Change = 1.5 is for 6 mins. So, what is the call rate for per min.

1.5 / 6 = 15 /60 = 0.25

Now find out the constant : 10*0.25 = 2.5

So, standard connection rate = 2.90 - 2.05 = 0.40

So charge for 13 mins : 13*0.25 + 0.4 = 3.25 + 0.4 = 3.65

The best answer is D.
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Re: The price of a phone call consists of a standard connection [#permalink] New post 11 Aug 2018, 16:43
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Explanation

Since “the price of a phone call consists of a standard connection fee, which is a constant, plus a per-minute charge,” write a formula, using variables for the unknown information. Let c equal the connection fee and r equal the per-minute rate:

\(2.90 = c + r(10)\)
\(4.40 = c + r(16)\)

Now, either substitute and solve or stack and combine the equation. Note that there is one c in each equation, so subtracting is likely to be fastest:

\(4.40 = c + 16r\)
\(- (2.90 = c + 10r)\)

\(1.50 = 6r\)

\(r = 0.25\)

The calls cost 25 cents per minute. Note that most people will next plug r back into either equation to find c, but c isn’t necessary to solve!

A 10-minute call costs \(\$2.90\). That \(\$2.90\) already includes the basic connection fee (which is a constant) as well as the per-minute fee for 10 minutes. The problem asks how much a 13-minute call costs. Add the cost for another 3 minutes ($0.75) to the cost for a 10-minute call ($2.90): \(2.90 + 0.75 = \$3.65\).

In fact, both the 10-minute and 16-minute calls include the same connection fee (which is a constant), so a shortcut can be used to solve. The extra 6 minutes for the 16-minute call cost a total of $4.40 – $2.90 = $1.50. From there, calculate the cost per minute (1.5 ÷ 6 = 0.25) or notice that 13 minutes is halfway between 10 minutes and 16 minutes, so the cost for a 13-minute call must also be halfway between the cost for a 10-minute call and the cost for a 16-minute call. Add half of $1.50, or $0.75, to $2.90 to get $3.65.
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Re: The price of a phone call consists of a standard connection [#permalink] New post 21 Jan 2019, 17:51
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sandy wrote:
The price of a phone call consists of a standard connection fee, which is constant, plus a per minute charge. A 10-minute call costs $2.90 and a 16-minute call costs $4.40. How much does a 13-minute call cost?

(A) $3.55
(B) $3.57
(C) $3.58
(D) $3.65
(E) $3.77


Letting f = the standard connection fee and n = the per-minute charge, we can create two equations, one for the 10-minute call and one for the 16-minute call::

f + 10n = 2.90

and

f + 16n = 4.40

Subtracting the first equation from the second, we have:

6n = 1.50

n = 0.25 (This is the per-minute charge)

Substituting 0.25 for n into the first equation, we see that f is:

f + 2.5 = 2.90

f = 0.4 (This is the fixed fee)

So a 13-minute call costs 0.4 + 13 x 0.25 = $3.65.

Answer: D
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Re: The price of a phone call consists of a standard connection   [#permalink] 21 Jan 2019, 17:51
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