For the tea question:
Let y = number of packets of tea
Let x = number of people at home
Before the grandmother arrived, in 5 weeks they bought 1 packet of tea per week, so 5y.
After the grandmother arrived, in 5 weeks they bought 1 packet of tea for 4 weeks and 2 packets on the final week, so 6y.
Before the grandmother arrived, they used one spoonful of tea per person and one for the pot, so x + 1 spoonfuls of tea.
After the grandmother arrived, they continued to use one spoonful of tea per person and one for the pot, so x + 2 spoonfuls of tea.
Therefore,
5y = x + 1 (equation 1)
and
6y = x + 2 (equation 2)
We now have a pair of simultaneous equations which can be solved.
Multiplying equation 1 by 6 gives, 30y = 6x + 6
Multiplying equation 2 by 5 gives, 30y = 5x + 10
Both of the right hand sides of these 2 equations equal 30y, so therefore they also equal each other, so,
6x + 6 = 5x + 10
Rearranging this equation gives,
6x - 5x = 10 - 6
So x = 4 and the answer is A.