0
$\begingroup$

I have a question as a problem.

Jack has gone to a trip and come back and when his friend asked the weather during Jack's trip, he answered as;

  • There were $10$ days which morning was sunny.
  • There were $7$ days which afternoon was sunny.
  • When afternoon was rainy, morning was sunny.
  • It rained totally $15$ times on morning or on afternoon.

So how many days did Jack spend for his trip according to information above?

I found the answer is 16. The answer on the book says 17. Thats why i confused. Thank you.

  • 0
    Are we to assume sunny and rainy are the only two options? – 2017-02-06
  • 0
    Must the weather be sunny or rainy? Or may it be foggy or snowy? – 2017-02-06
  • 0
    Yes they are two options. Just rainy or sunny. – 2017-02-06

3 Answers 3

0

Hints: Consider the four sets:

$SS$, $SR$, $RS$, and $RR$ ($SR$ means sunny in the morning and rainy in the afternoon).

From the given information, you know that

  • $|SS|+|SR|=10$ because $10$ days were sunny in the morning.

  • $|SS|+|RS|=7$ because on $7$ days, the afternoon was sunny.

  • $|RR|=0$ because if it were rainy in the afternoon, then it would have to be sunny in the morning.

  • $|SR|+|RS|+2|RR|=15$ because it rained on $15$ days.

From this, can you figure out the total number of days: $|SS|+|SR|+|RS|+|RR|$?

  • 0
    I found also 16. The answer on the book says 17. Thats why i confused. Do you agree with me? – 2017-02-06
  • 0
    This would be good to add your original question. I think that $16$ also works. – 2017-02-06
  • 0
    Don't forget if it rained in the morning and afternoon that is 2 times it rained by only 1 day. I get 17. S that last line should be |sr| + |rs| + 2|rr| = 15. – 2017-02-06
  • 0
    @fleablood Thanks for the catch. However, from the way that the question was worded, $|RR|=0$, so it doesn't make a difference! – 2017-02-06
  • 0
    Oops. That was an error I made. Somehow I got that |RS| was 0. Not |RR|. If so, you get that |SS| = 7,|SR| = 3, and |RR| = 6 and ... dang, that'd still be 16. Okay, not sure why I made those two mistakes. – 2017-02-06
  • 0
    The only issue is that, perhaps, we're misinterpreting the condition "When afternoon was rainy, morning was sunny." and that's how the answer is $17$. – 2017-02-06
  • 0
    For which interpretation of that condition, can the solution be 17, do you think? – 2017-02-06
  • 0
    I can find no reasonable interpretation that leads to $17$. – 2017-02-06
0

Assume that rainy and sunny are the only to options we have:

$X =$ number of all sunny days

$Y = $ number of sunny mornings, rainy afternoons

$Z = $ number of all rainy days.

$A = $ number of rainy mornings and sunny afternoons.

There were 10 days which morning was sunny $\implies X + Y = 10$

There were 7 days which afternoon was sunny $\implies X + A = 7$

When afternoon was rainy, morning was sunny $\implies Z = 0$

It rained totally 15 times on morning or on afternoon $\implies Y + A + 2Z = 15$

Solve for $X + Y + Z + A$.

0

Let $r$ and $s$ be the number of rainy and sunny mornings, respectively, and likewise let $R$ and $S$ be the number of rainy and sunny afternoons. Clearly $r+s=R+S$, since each side counts the total number of days in the trip, which is the number we're after.

The first two bullet points tell us $s=10$ and $S=7$. The final two bullet points tell us $r+R=15$. (That is, it can't rain both morning and afternoon, so the total number of days with rain is $r+R$.) This gives us enough to solve for $r$ and $R$: From $r+10=R+7$ we have $R=r+3$, which gives us $2r+3=15$, hence $r=(15-3)/2=6$ and $R=6+3=9$. And thus the total number of days in the trip is $6+10=9+7=16$.

I don't see any way to interpret the problem so as to get $17$ as the answer. The book seems to have made a mistake.

  • 0
    Thank you Barry Cipra. I was thinking that third condition means that if afternoon is rainy, the next morning will be sunny? – 2017-02-06
  • 0
    @layout789, Hmm, interesting interpretation. I don't think it can get you to $17$ though. (Note, all three answers so far interpret the third condition in the same way.) – 2017-02-06
  • 0
    I know that I am forcing a little. – 2017-02-06