SOLUTION: The weather during the Forburg's vacation was very strange. It was cloudy on 13 different days, but it was never cloudy for an entire day. Cloudy mornings were followed by clear

Question 152343: The weather during the Forburg's vacation was very strange.
It was cloudy on 13 different days, but it was never cloudy for an entire day.
Cloudy mornings were followed by clear afternoons.
Cloudy afternoons were preceded by clear mornings.
There were 11 clear mornings and 12 clear afternoons in all.
How long was the vacation?
Answer by mducky2(62) (Show Source):
You can put this solution on YOUR website!
Let's label cloudy and clear mornings and afternoons.
Cloudy mornings: M_cloudy
Cloudy afternoons: A_cloudy
Clear mornings: M_clear
Clear afternoons: A_clear

We know that there are only 13 cloudy days. Since it was never cloudy for an entire day, we know that the sum of the cloudy afternoons and cloudy mornings equal the number of cloudy days:
M_cloudy + A_cloudy = 13

We also know the number of clear mornings and clear afternoons:
M_clear = 11
A_clear = 12
M_clear + A_clear = 23

Since there is one morning and one afternoon per day, the total number of mornings plus the total number of afternoons will equal twice the total number of days:
(M_cloudy + A_cloudy + M_clear + A_clear)/2
= (13 + 23)/2
= 36/2
= 18

There were 18 days during Forburg's vacation.