NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Example 3

NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Example 3

Question:

Champa went to a ‘Sale’ to purchase some pants and skirts. When her friends asked her how many of each she had bought, she answered, “The number of skirts is two less than twice the number of pants purchased. Also, the number of skirts is four less than four times the number of pants purchased”. Help her friends to find how many pants and skirts Champa bought.

Given:

  • Let the number of pants Champa bought be \( x \).
  • Let the number of skirts Champa bought be \( y \).
  • The number of skirts is two less than twice the number of pants: \( y = 2x - 2 \).
  • The number of skirts is four less than four times the number of pants: \( y = 4x - 4 \).

To Find:

  • The number of pants (\( x \)) and skirts (\( y \)) that Champa bought.

Formula:

  • Form equations based on the statements:
  • \( y = 2x - 2 \)
  • \( y = 4x - 4 \)
  • Solve the system of linear equations to find \( x \) and \( y \).

Solution:

Step 1: Let the number of pants be \( x \) and the number of skirts be \( y \).

Step 2: Write the first condition as an equation:

$$ y = 2x - 2 \quad \cdots (1) $$

Step 3: Write the second condition as an equation:

$$ y = 4x - 4 \quad \cdots (2) $$

Step 4: Equate the right sides of equations (1) and (2):

$$ 2x - 2 = 4x - 4 $$

Step 5: Rearranging the terms:

$$ 2x - 2 = 4x - 4 \\ 2x - 4x = -4 + 2 \\ -2x = -2 $$

Step 6: Solve for \( x \):

$$ -2x = -2 \\ x = 1 $$

Step 7: Substitute \( x = 1 \) into equation (1) to find \( y \):

$$ y = 2x - 2 \\ y = 2 \times 1 - 2 \\ y = 2 - 2 = 0 $$

Step 8: Therefore, Champa bought 1 pant and 0 skirts.

Result:

  • Champa bought 1 pant and 0 skirts.
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