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.

Solution

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=3800−7x6 … (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(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=3006 ⇒ y = 50 Hence, cost of each bat = Rs 500 and cost of each balls = Rs 50.  Mathematics

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