It was vacation time on Long Island. We went to the beach some days
and went sailing other days. We could not seem to find the time to do
both activities in one day and on some days the weather kept us from
doing either activity.

In 2005 we did not get to the beach on 7 days and we did not go
sailing on 12 days. But we did do one or the other on 13 days. How
many days did we spend on Long Island?

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Request for Question Clarification by efn-ga on 09 Jan 2006 19:30 PST

Is this a school assignment?

Hi


Spoiler space for those who want to think about it...







Answer:

16 days

You went sailing for 4 days (and thus not for the other 12)
You went on the beach for 9 days (and thus not for the other 7)

Ratty

Not being as mentally agile as ratty, I had to write down the four
things I didn't know - abbreviated as T, B, S, and N. There was enough
information to write four simple equations using two or more of these
unknowns; then solving for T was also simple.

I agree with ratty and did the same as brix24 did (but with just 3 equations)

B = Beach Days
S = Sailing Days
T = Total

1) S + B = 13     ("But we did do one or the other on 13 days")
2) T - 7 = B        ("we did not get to the beach on 7 days")
3) T - 12 = S      ("we did not go sailing on 12 days")

Substitution method

I)    Using equation 1)   S = 13 - B

II)   Using 2)   T = B + 7
      Using 3)   T = S + 12
      Then B + 7 = S + 12    Then S = B -5

III)  Using I and II
	13 - B = B - 5
	18 = 2B
	B = 9

IV) Using I and III
	S = 13 - 9 = 4

V) T = S + 12    Then T = 16
   or T = B + 7    Then T = 16

You went sailing for 4 days
You went to the beach for 9 days


Answer:  You spent 16 days on Long Island