Q3(iii):

Form the pair of linear equations for the following problems and find their solution by substitution method. (iii) The coach of a cricket team buys 7 bats and 6 balls for ` 3800. Later, she buys 3 bats and 5 balls for ` 1750. Find the cost of each bat and each ball.

Given:

1. The cost of 7 bats and 6 balls is ₹ 3800.

2. The cost of 3 bats and 5 balls is ₹ 1750.

To Find:

The cost of one bat and the cost of one ball.

Step 1: Defining Variables

Let the cost of one bat be $x$ and the cost of one ball be $y$.

Step 2: Formulating the Linear Equations

Based on the given information, we can construct the following system of linear equations:

Equation (1): $7x + 6y = 3800$

Equation (2): $3x + 5y = 1750$

Step 3: Applying the Substitution Method

From Equation (2), express $x$ in terms of $y$:

$3x = 1750 - 5y$

$x = \frac{1750 - 5y}{3}$ --- (Equation 3)

Step 4: Substituting Equation (3) into Equation (1)

Substitute the value of $x$ from Equation (3) into Equation (1):

$7\left(\frac{1750 - 5y}{3}\right) + 6y = 3800$

Multiply the entire equation by 3 to eliminate the denominator:

$7(1750 - 5y) + 18y = 3800 \times 3$

$12250 - 35y + 18y = 11400$

Combine the $y$ terms:

$12250 - 17y = 11400$

Isolate the variable $y$:

$-17y = 11400 - 12250$

$-17y = -850$

$y = \frac{-850}{-17}$

$y = 50$

Step 5: Finding the value of $x$

Substitute $y = 50$ into Equation (3):

$x = \frac{1750 - 5(50)}{3}$

$x = \frac{1750 - 250}{3}$

$x = \frac{1500}{3}$

$x = 500$

Step 6: Verification

Check the values in Equation (1): $7(500) + 6(50) = 3500 + 300 = 3800$. (Correct)

Check the values in Equation (2): $3(500) + 5(50) = 1500 + 250 = 1750$. (Correct)

Final Answer: The cost of one bat is ₹ 500 and the cost of one ball is ₹ 50.