Problema Solution
The camel can carry 1000 bananas at a time. she has 3000 bananas. where she needs to drop them off is 1000 miles away. she eats 1 banana for every mile she goes. out of the 3000 bananas what is the largest number of bananas she can get to her destination?
Answer provided by our tutors
We will assume the camel eats the banana after making 1 mile.
At MI#0, we have 3000 bananas.
The maximum bananas the camel can carry is 1000 so the camel must at least make 3 trips from the start point. (Leave #0, Return to #0, Leave #0, Return to #0, Leave #0).
If we move just 1 mi, we need 1 banana for each step mentioned above thus making a total of 5 bananas for each mi.
We continue making 3 trips until we reach a banana count of 2000.
3000 – 5*d = 2000 => d = 200
At #200 mi, we will have 2000 bananas
At this point, we only need to make 2 trips (Leave #200, Return to #200, Leave #200). This will cost 1 banana for each step thus making a total of 3 bananas for each mile.
We continue making 2 trips until we reach a banana count of 1000.
2000 – 3*d = 1000 => d = 333 mi
2000 - 999 = 1001
At#(200+333) = #533 mi, we will have 1001 bananas
Next #534 mi there will be 999 banana and 1 banana left behind. There is not point that the camel goes back for only 1 banana since it will need to make 2 miles (eat 2 banana) to get just 1 banana, so its better to leave that 1 banana behind.
At #534 mil we have 999 bananas.
At this point, we need to make one trip so the camel just carries everything and marches toward the market.
Remaining mi = 1000 – 534 = 466 mi. Bananas needed = 466.
Therefore, the bananas remaining once the camel reaches the market is 999 – 466 = 533.