The Horse Traders' Puzzle
Bhāskarāchārya's problem: money, horses and a debt.
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One man has ₹300 and 6 horses; the other has 10 horses and a debt of ₹100. They are equally rich. What does a horse cost?
See how algebra grew in India and travelled the world, read equations in old Indian notation, and use Brahmagupta's formula for Ax + B = Cx + D.
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Bīja means seed: the answer is hidden inside the unknown.
In ancient India, algebra was called bījagaṇita. Bīja means seed. Just as a tree is hidden inside a seed, the answer to a problem is hidden inside the unknown number. Solving is like helping the tree grow, step by step.
Bhāskarāchārya's problem: money, horses and a debt.
One man has ₹300 and 6 horses; the other has 10 horses and a debt of ₹100. They are equally rich. What does a horse cost?
Two historical problems solved with equations.
Problem 1 (Example 16, p. 183). From Bījagaṇita by Bhāskarāchārya (1150 CE): one man has ₹300 and 6 horses. Another has 10 horses and a debt of ₹100. They are equally rich. What is the price of one horse?
Recall the story of algebra.
Bīja means…
Brahmagupta's rule solves Ax + B = Cx + D in one line.
A systematic way to solve problems with one unknown was first proposed by Aryabhata (499 CE), and Brahmagupta set it out in 628 CE.
Four equations solved in one line each.
Problem. Solve each equation with x = (D − B)/(A − C). (Textbook p. 184)
Use the formula on four equations.
7x + 2 = 4x + 14. x = ( − 2)/(7 − ) = .
9x − 5 = 5x + 7. x = .
3x + 10 = 5x + 2. x = .
The horses: 6x + 300 = 10x − 100. x = (−100 − 300)/(6 − 10) = .