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A Pinch of History

In the 12th century CE, a well-known mathematician named Bhaskara
lived in India. His contributions to mathematics were so outstanding
that the illustrious Bhaskara, whose accomplishments are admired
by the learnt and the wise, is described as a triumphant figure in a
mediaeval inscription found in an Indian temple. He is a poet of holy
worth and glory, like a peacock’s crest.
As was the norm in his era’s India, Bhaskara wrote all of his
mathematical writings in verse. Lilavati, his most endearing novel, was
written for his daughter, who was known as Lilavati (The Beautiful). It is
filled with fascinating algebraic poetry. Here is one poem from Lilavati: Bhaskara II (Bhaskaracharya)
(1114–1185)
A fifth part of a swarm of bees came to rest
on the flower of Kadamba,
a third on the flower of Silinda.
Three times the difference between these two numbers
flew over a flower of Krutaja,
and one bee alone remained in the air,
attracted by the perfume of a jasmine in bloom,
Tell me, beautiful girl, how many bees were in the swarm?
The number of bees can be found by using the concept of a linear equation.

Practice Time 2B

1. Solve the following equations and verify your answers.
15 x − 4
( a) – 7x = 9x + 4 (b) + 2 = − 5 x ( c) 4x – (2x – 5) = 3x + 1
4 3 5
13 8x 2 1
( d) x += − 3 ( e) –3(2x + 2) = 5(x – 3) – 2 (f) x + ( x − 5 =) 3
8
5 5 3 2
2. Solve the following equations.
2x − 5 3x − 2 2x − 7 1 − x
( a) 0.3(6 + m) = 0.4(8 – m) (b) + = 1 ( c) − = 9
3 2 3 2
m m − 1 1 m − 2 x + 2 x + 1 x − 3
( d) − = − ( e) − = − 1 ( f) 2(1.5x + 2.5) = 0.5x + 3
4 2 8 3 3 5 4
3. The sum of three consecutive integers is 10 more than the twice the smallest of the integers. Find
the integers.
1 1
4. Rahul has certain number of chocolate pies, he gave of chocolate pies to his brother and of
3 6
them to his friend. He was then left with 30 chocolate pies. How many chocolate pies did he give to
each one.
3
5. A number consists of two digits, whose sum is 9. If the digits are reversed, the new number is of
the original number. Find the number. 8

6. The sum of two positive integers is 98. The integers are in the ratio of 3 : 4. Find the integers.
7. A number consists of two digits whose sum is 7. If 45 is added to the number, the digits are reversed.
Find the number.

45 Linear Equations in One Variable