Page 93 - Mathematics Class - X

PROJECT 6

AIM
Application of algebra in day-to-day life.

DESCRIPTION

Algebra arise in several situations in the world around us and in different fields of mathematics. Let us consider
an example.

A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that
the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that
day. If the total cost of production on that day was ` 90, find the number of articles produced and the cost of each
article.
Given: The total cost of production = ` 90

Let the number of pottery articles produced be x.

Therefore, cost of production of each article = ` (2x + 3)
The total cost of production = No. of pottery articles produced × cost of production

According to the question,

90 = x(2x + 3)
⇒ 2x²+ 3x – 90 = 0

⇒ 2x² + 15x – 12x – 90 = 0

⇒ x(2x + 15) – 6(2x + 15) = 0
⇒ (2x + 15)(x – 6) = 0

Now 2x + 15 = 0

⇒ 2x = – 15
⇒ x = – 15/2

⇒ x – 6 = 0

⇒ x = 6
⇒ x = – 15/2

or x = 6

As the number of articles produced can only be a positive integer, therefore, x can only be 6.
Hence, number of articles produced = 6

Cost of each article = 2 × 6 + 3 = ` 15

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