the coach of a cricket team buys 4 bats and 1 ball for rs. 2050. later, she buys 3 bats and 2 balls for 1600. find the cost of each bat and each ball.
Given problem:
A cricket coach first buys 4 bats and 1 ball for a total of Rs. 2050. Later, she buys 3 bats and 2 balls for Rs. 1600. We need to find the cost of each bat and each ball.
Solution:
Let’s denote the cost of one bat as ( x ) rupees and the cost of one ball as ( y ) rupees.
According to the first statement:
4 bats + 1 ball = Rs. 2050
This can be represented as the equation:
(4x + y = 2050) —(1)
According to the second statement:
3 bats + 2 balls = Rs. 1600
This can be represented as the equation:
(3x + 2y = 1600) —(2)
Now, we have a system of two equations with two variables. We can solve this system of equations to find the values of (x) and (y).
From equation (1), we can express (y) in terms of (x):
[ y = 2050 - 4x ] —(3)
Substitute equation (3) into equation (2) to solve for (x):
[ 3x + 2(2050 - 4x) = 1600 ]
[ 3x + 4100 - 8x = 1600 ]
[ -5x = -2500 ]
[ x = 500 ]
Now that we have found the cost of one bat ((x = 500)), we can substitute this back into equation (3) to find the cost of one ball:
[ y = 2050 - 4(500) ]
[ y = 2050 - 2000 ]
[ y = 50 ]
Therefore, the cost of each bat is Rs. 500, and the cost of each ball is Rs. 50.