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Question 157362This question is from textbook
: 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?
This question is from textbook
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! i have no idea if this is correct, but this is what i think.
let c = cloudy and x = clear.
each day is either cx, xc, or xx
cx is cloudy in the morning.
xc is cloudy in the afternoon.
xx is clear all day.
if it is cloudy, it is only cloudy in the morning or in the afternoon, never all day (given).
13 days are either cx or xc.
11 days are either cx or xx.
12 days are either xc or xx.
we have 23 total days that are either xc or cx or xx.
we have 13 total days that are either cx or xc.
23 - 13 = 10 days that have to be xx.
total days in the vacation must be 23.
i tried 3 scenarios and they all came out the same.
scenario 1 is 11 cx and 2 xc.
that left 10xx.
scenario 2 is 12xc and 1 cx.
that also left 10xx.
scenario 3 is 6cx and 7xc.
that also left 10xx.
i have to go with 23 total vacation days being a combination of cx, xc, or xx.
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