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 Rs 3800. Later, she buys 3 bats and 5 balls for Rs 1750. Find the cost of each bat and each ball.
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
6y = 3800 – 7x
Dividing by 6, we get
y = (3800 – 7x)/6 … (i)
Given that she buys 3 bats and 5 balls for Rs 1750 later.
3x + 5y = 1750
Putting the value of y
3x + 5 ((3800 – 7x)/6) = 1750
Multiplying by 6, we get
18x + 19000 – 35x = 10500
-17x =10500 - 19000
-17x = -8500
x = - 8500/- 17
x = 500
Putting this value in equation (i) we get
y = ( 3800 – 7 × 500)/6
y = 300/6
y = 50
Hence cost of each bat = Rs 500 and cost of each balls = Rs 50.
