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The price of a phone call consists of a standard connection fee, which

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The price of a phone call consists of a standard connection fee, which  [#permalink]

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New post 27 Jul 2018, 01:32
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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

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Re: The price of a phone call consists of a standard connection fee, which  [#permalink]

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New post 27 Jul 2018, 02:50
1
Let s be the standard connection fee and c be the minute charge

A 10-minute call costs $2.90 = 290 cents

=> s + 10c = 290 ------- (1)

16-minute call costs $4.40 = 440 cents

=> s + 16c = 440 ------- (2)

Subtracting 1 from 2

6c = 150

=> c = 25

Substituting the value of c in 1

=> s + 250 = 290

=> s = 40

13-minute call would cost => 40 + 13(25) = 365 cents = $3.65

Hence option D
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Re: The price of a phone call consists of a standard connection fee, which  [#permalink]

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New post 27 Jul 2018, 02:58
Ans: D
As one method is already mentioned above.. Idea is same here but might be a bit short.
Given : Call cost(C ) = fixed Charge (F)+ Minutes(minutes charge) (nM) : where n is number of minutes.
so from stem:
2.90 = F+9M ----(Eq.1)
4.40 = F+15M ----(Eq.2): and we need to find F+12M = ?? ----(Eq.3)
now we can start solving and do the calculations by finding one value and then getting second or just look at the equations. if we add Eq.1 & Eq.2
2.90 = F+9M
4.40 = F+15M
---------------
7.30 = 2F + 24M : gives is 3.65 =F+12M ans..

Bunuel 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

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Re: The price of a phone call consists of a standard connection fee, which  [#permalink]

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New post 27 Jul 2018, 03:29
Let:
F be be the fixed connection cost
V be variable cost per minute

We get two equations:
F+10V=2.9
F+16v=4.4

Solve it and F=0.4 V=0.25

0.4+13*0.25=3.65

IMO
Ans: D
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Re: The price of a phone call consists of a standard connection fee, which  [#permalink]

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New post 02 Oct 2018, 21:40
Hi All,

We're told that 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. We're asked for the cost of a 13-minute call. This question can be solved in a couple of different ways - and there's a great 'rate shortcut' that you can use to avoid some of the extra math that comes with certain approaches.

Since there's a standard connection fee, we know that the difference between the costs of two calls is solely due to the number of minutes in the call. With the given information (about a 10-minute call and a 16-minute call), the difference in price comes down to the 6 minute difference in the length of the calls. Thus, the extra 6 minutes cost an extra $4.40 - $2.90 = $1.50. We're asked for the cost of a 13-minute call - which is exactly 'halfway' between those two prices. Half of $1.50 is $0.75, so we can add that to the cost of a 10-minute call to find the cost of the 13-minute call. $2.90 + $0.75 = $3.65

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Re: The price of a phone call consists of a standard connection fee, which  [#permalink]

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New post 03 Oct 2018, 17:59
Bunuel 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

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

f + 2.5 = 2.90

f = 0.4

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

Alternate solution:

If we let m = the per-minute charge, x = the number of minutes, b = the standard connection fee, and y = the total cost of an x-minute call, we will have y = mx + b. As we can see, this is a line, and the ordered pairs (10, 2.90) and (16, 4.40) are on this line. We are looking for the y-value when x = 13. We can observe that 13 is exactly halfway between 10 and 16; therefore, the y-value should be exactly halfway between 2.90 and 4.40 also. Thus y = (2.90 + 4.40)/2 = 7.30/2 = 3.65.

Answer: D
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The price of a phone call consists of a standard connection fee, which  [#permalink]

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New post 04 Oct 2018, 06:52
Bunuel 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

\(? = f + 13c\,\,\,\,\left[ \$ \right]\)

The constant fee (f) and the minute-charge (c) will be considered in CENTS. (Amounts in cents are always integers!)

\(\left\{ \matrix{
\,f + 10c = 290 \hfill \cr
\,f + 16c = 440 \hfill \cr} \right.\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,\,2f + 26c = 290 + 440\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{focus}}\,!} \,\,\,\,\,\,? = {{2f + 26c} \over 2} = 145 + 220 = 365\,\,\,\,\,\,\left[ {\,{\rm{cents}}\,} \right]\)

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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