Solution:
Let
- x denote the number of days we jogged in the morning and stayed at home in the evening;
- y denote the number of days we played tennis in the evening and did nothing in the morning; and
- z denote the number of days we neither jogged nor played tennis.
Then,
y +
z = number of mornings we did nothing = 12
x +
z = number of evenings we stayed at home = 15
x +
y = number of days we jogged or played tennis = 11
Adding the above three equations and dividing both sides by 2 gives
x +
y +
z = 19
Since there are only three types of days, the total number of days I stayed with my cousin is their sum, i.e., 19.
Food for thought:
Can you solve this puzzle using a Venn diagram with two intersecting sets? Could the two sets be "days we did nothing in the morning" and "days we stayed at home in the evening"?
