Trip Day Problem

Question

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.

Answer 1

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: $|SS|+|SR|+|RS|+|RR|$?

Answer 2

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 $X + Y + Z + A$.

Answer 3

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.