For a basic monthly fee of F yen (¥F), Noako's

Hi jjjinapinch,

To start, I think that there's a 'typo' in this question. In the Official Guide, we are asked to find the value of F (not M).

We're told that on Noako's cell phone plan, he can make UP TO 420 minutes of calls for a flat monthly fee of F yen. For EACH of X additional minutes used though, an additional charge of M yen occurs, making the total charge for the month T yen, where
T = F + (X)(M). We're asked for the value of F.

1) Naoko used 450 minutes on the first month and the total charge for the month was 13,755 yen.

With this information, we know that 30 'extra' minutes were used (above the 420 that come with flat fee), so we can create the following equation:
13,755 = F + (30)(M)

Unfortunately, we have 2 variables and just 1 equation to work with, so there are a multitude of possible values for F.
Fact 1 is INSUFFICIENT

2) Naoko used 400 minutes on calls the second month and the total charge for the month was 13,125 yen.

With this information, we know that NO extra minutes were used (just 400 minutes of the 420 monthly 'limit' of the flat fee were used), thus we can create the following equation:
13,125 = F + (0)(M)

Thus, F must equal 13,125
Fact 2 is SUFFICIENT

Final Answer: B

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Rich