A care taker has to provide food for 40 people.he decide to give them a choice of chicken or fish.each chicken can provide for up to 4 people and each fish for up to 8 people.he decides to use not more than 6 chicken and also that the number of fish would not exceed the number of chicken used

1 answer

To provide food for 40 people using a combination of chicken and fish, the care taker can use a maximum of 6 chickens and the number of fish should not exceed the number of chickens.

Let's say the care taker uses x chickens and y fish.

Given that each chicken can feed up to 4 people and each fish can feed up to 8 people, we can form the following equations:

4x + 8y = 40 (total number of people)
x ≤ 6 (maximum number of chickens)
y ≤ x (number of fish does not exceed number of chickens)

Now, we can determine the possible combinations of x and y that satisfy these conditions:

For x = 1, y can be 0, 1, or 2
For x = 2, y can be 0, 1, or 2
For x = 3, y can be 0, 1, 2, or 3
For x = 4, y can be 0, 1, 2, 3, or 4
For x = 5, y can be 0, 1, 2, 3, 4, or 5
For x = 6, y can be 0, 1, 2, 3, 4, 5, or 6

Therefore, the possible combinations of chickens and fish that satisfy the conditions are:
(1 chicken, 0 fish)
(1 chicken, 1 fish)
(1 chicken, 2 fish)
(2 chickens, 0 fish)
(2 chickens, 1 fish)
(2 chickens, 2 fish)
(3 chickens, 0 fish)
(3 chickens, 1 fish)
(3 chickens, 2 fish)
(3 chickens, 3 fish)
(4 chickens, 0 fish)
(4 chickens, 1 fish)
(4 chickens, 2 fish)
(4 chickens, 3 fish)
(4 chickens, 4 fish)
(5 chickens, 0 fish)
(5 chickens, 1 fish)
(5 chickens, 2 fish)
(5 chickens, 3 fish)
(5 chickens, 4 fish)
(5 chickens, 5 fish)
(6 chickens, 0 fish)
(6 chickens, 1 fish)
(6 chickens, 2 fish)
(6 chickens, 3 fish)
(6 chickens, 4 fish)
(6 chickens, 5 fish)
(6 chickens, 6 fish)

The care taker can choose one of the above combinations to provide food for 40 people with a maximum of 6 chickens and the number of fish not exceeding the number of chickens.