Question

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

Answer 1

Let cost of each bat = Rs x
Cost of each ball = Rs y
Given that coach of a cricket team buys 7 bats and 6 balls for Rs 3800.
7x + 6y = 3800
$\Rightarrow$ 6y = 3800 - 7x
Dividing by 6, we get
$y=\frac{3800-7x}{6}$ … (i)
Given that she buys 3 bats and 5 balls for Rs 1750 later.
3x + 5y = 1750 ----(ii)
Substituting the value of y in equation (ii), we get
$3x+5\frac{(3800-7x)}{6}=1750$
Multiplying by 6, we get
$\Rightarrow$ 18x + 19000 - 35x = 10500
$\Rightarrow$ -17x =10500 - 19000
$\Rightarrow$ -17x = -8500
$\Rightarrow$ $x=\frac{-8500}{-17}$
$\Rightarrow$ x = 500
Putting this value in equation (i), we get
$y=\frac{(3800-7\times 500)}{6}$
$\Rightarrow$ $y=\frac{300}{6}$
$\Rightarrow$ y = 50
Hence, cost of each bat = Rs 500 and cost of each balls = Rs 50.