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The price of a phone call consists of a standard connection
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25 Jul 2018, 17:20
25 Jul 2018, 17:20
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Question Stats:
86% (01:56) correct
13% (02:18) wrong based on 84 sessions
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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
(A) $3.55
(B) $3.57
(C) $3.58
(D) $3.65
(E) $3.77
Re: The price of a phone call consists of a standard connection
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25 Jul 2018, 23:08
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
(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.
General Discussion
Re: The price of a phone call consists of a standard connection
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11 Aug 2018, 16:43
11 Aug 2018, 16:43
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Expert Reply
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.
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.
