# Math Help - How long did i stay

1. ## How long did i stay

I visited my friends home during my holidays.Our schedule went like this. We went for a walk in morning and played badminton in the evening. However due to the tiring nature of these, we did only 1 of them each day, i.e either walked or played Badminton. On some days we did neither!On 11 mornings we did nothing, 10 evenings we did nothing, we walked or played Badminton on a total of 11days. How long did i stay@ my friends place?

The attempt at a solution
1 activity each day.
total activities=11 events=11 days (morning+evening)
11 mornings+10 eveings did nothing= 10 days + 1 morning.
so, i guess.. 11+11=22 days??

pls confirm the same.

2. activity of 11 days = 11 Morn(M) and 11 evenings(E)
i.e. walk 6 M AND badminton 5 Evenings. This leaves 5 M AND 6 E.

OR

walk 5M and Badminton 6 E. this leaves 6M and 5E- no activity.

But if we consider 2nd possibility;
now, 11 M and 10 E did nothing, including the activity days.
this leaves full day of no activity - 5 M and 5 E= 5 days

hence,
the total days= 11+5days=16 days.

pls confirm.
yahoo.

3. Hello scotyard
Originally Posted by scotyard
activity of 11 days = 11 Morn(M) and 11 evenings(E)
i.e. walk 6 M AND badminton 5 Evenings. This leaves 5 M AND 6 E.

OR

walk 5M and Badminton 6 E. this leaves 6M and 5E- no activity.

But if we consider 2nd possibility;
now, 11 M and 10 E did nothing, including the activity days.
this leaves full day of no activity - 5 M and 5 E= 5 days

hence,
the total days= 11+5days=16 days.

pls confirm.
yahoo.
I agree with your answer of 16 days, but I have a simple algebraic solution that doesn't depend on guesswork (which your solution seems to use!).

Suppose that you did an activity on $x$ mornings. Then you did an activity on $(11-x)$ evenings, since you did 11 activities altogether.

Suppose further that you stayed a total of $y$ days. Then you did no morning activity on $(y-x)$ days and no evening activity on $y - (11-x) = y+x - 11$ days. This gives two equations:

$y - x = 11$

$y+x-11 = 10$

From which we get $x = 5,\, y = 16$.