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Sub 505 Level|   Word Problems|            
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carcass
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How do you know not to primarily find out the duration of the call first and then calculate the costs for the 11 pm call? Bunuel's solution is easy and quick, but how to get the hint at first sight to attack this problem exactly this way? Thx for any comments, tips how to think through this problem.
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carcass wrote
Quote:

For telephone calls between two particular cities, a telephone company charges $0.40 per minute if the calls are placed between 5:00 a.m. and 9:00 p.m. and $0.25 per minute if the calls are placed between 9:00 p.m. and 5:00 a.m. If the charge for a call between the two cities placed at 1:00 p.m. was $10.00, how much would a call of the same duration have cost if it had been placed at 11.00 p.m.?

(A) $3.75

(B) $6.25

(C) $9.85

(D) $10.00

(E) $16.00

AnnKatrin wrote
Quote:
How do you know not to primarily find out the duration of the call first and then calculate the costs for the 11 pm call? Bunuel's solution is easy and quick, but how to get the hint at first sight to attack this problem exactly this way? Thx for any comments, tips how to think through this problem.
AnnKatrin , Bunuel did exactly what you described:
1) "[first] find out the duration of the call"; and
2) "then calculate the costs for the 11 pm call."

He first calculated the duration of the call at 1 p.m (total cost, divided by cost per minute, yields number of minutes):
Quote:
Bunuel: A call between the two cities placed at 1:00 p.m. will be charges at $0.40 per minute, so $10.00 will be charged for 10/0.4 = 25-minute call.
With total minutes known, then he calculated the cost for the 11:00 p.m. call:
Quote:
25-minute call at $0.25 per minute will cost 25*0.25 = $6.25.
So you are spot-on about the method. You just didn't catch that Bunuel used that method. You don't need any tips on method here.

I'm going to bet you have tired eyes and just missed something. Easy to do. :-) Does that help?
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Call charges per minute
0.4(5am-9pm):0.25(9pm-5am)
These charges are in proportion 8:5.
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carcass
For telephone calls between two particular cities, a telephone company charges $0.40 per minute if the calls are placed between 5:00 a.m. and 9:00 p.m. and $0.25 per minute if the calls are placed between 9:00 p.m. and 5:00 a.m. If the charge for a call between the two cities placed at 1:00 p.m. was $10.00, how much would a call of the same duration have cost if it had been placed at 11.00 p.m.?

(A) $3.75

(B) $6.25

(C) $9.85

(D) $10.00

(E) $16.00

We can let m = the number of minutes for the call and create the equation:

0.4m = 10

m = 25

So if the call was placed at 11 pm, it would have cost 25 x 0.25 = 6.25 dollars.

Answer: B
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How do you know that the first call was placed between 5:00 am to 9:00 pm ?

Posted from my mobile device
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Shivani1297
How do you know that the first call was placed between 5:00 am to 9:00 pm ?

Posted from my mobile device

If the charge for a call between the two cities placed at 1:00 p.m. was $10.00...

The first call was at 1:00 p.m. not between 5 and 9.
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carcass
For telephone calls between two particular cities, a telephone company charges $0.40 per minute if the calls are placed between 5:00 a.m. and 9:00 p.m. and $0.25 per minute if the calls are placed between 9:00 p.m. and 5:00 a.m. If the charge for a call between the two cities placed at 1:00 p.m. was $10.00, how much would a call of the same duration have cost if it had been placed at 11.00 p.m.?

(A) $3.75

(B) $6.25

(C) $9.85

(D) $10.00

(E) $16.00

Let x = the duration (in minutes) of the call
For calls at $0.40 per minute, we can write: 0.4x = 10
Solve to get: x = 25
So, the original call lasted 25 minutes.

If the 25-minute call were placed at 11 pm (at $0.25 per minute) , the cost would = 25 x $0.25 = $6.25

Answer: B

Cheers,
Brent
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