A gentleman sent his friend with £100 to buy 100 cattle, with orders to give £5 for each Bullock, 20 Shillings for cows, and one Shilling for each sheep.

How many of each did his friend buy?

Note: Banneker lived in the eighteenth century when the word cattle was used to describe domesticated animals, including sheep, goats, cows, and bulls.   A shilling was 1/20 of a pound (£).



Solution to the Problem:


His friend bought 19 bulls, 1 cow, and 80 sheep.

Let b = # of bulls
Let c = # of cows
Let s = # of sheep

Then we can write two Diophantine equations (they have integer solutions):
b + c + s = 100
5b + c + s/20 = 100

c = 100 - b - s
So, 5b + (100 - b - s) + s/20 = 100
Then 80b = 19s.

The first integral solution is b = 19 and s = 80.
Substituting back in the first equation yields c = 1.


Correctly solved by:

1. Davit Banana Istanbul, Turkey
2. Aayan Shah Lalitpur, Nepal
3. Balaji V Sirkazhi, Tamilnadu, India
4. Kelly Stubblefield Mobile, Alabama
5. Dr. Hari Kishan D.N. College,
Meerut, Uttar Pradesh, India
6. Ivy Joseph Pune, Maharashtra, India
7. Veena Mg Bangalore, Karnataka, India
8. Colin (Yowie) Bowey Beechworth, Victoria, Australia