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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. Q.3(3)

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The third part of class10 math of exercise 3.3 i don’t know how to solve this question by easy way 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.

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1. Let the cost a bat be x and cost of a ball be y.

According to the question,

7x + 6y = 3800 â€¦â€¦â€¦â€¦â€¦â€¦. (I)

3x + 5y = 1750 â€¦â€¦â€¦â€¦â€¦â€¦. (II)

From (I), we get

y = (3800-7x)/6â€¦â€¦â€¦â€¦â€¦â€¦..(III)

Substituting (III) in (II). we get,

3x+5(3800-7x)/6 =1750

â‡’3x+ 9500/3 â€“ 35x/6 = 1750

â‡’3x- 35x/6 = 1750 â€“ 9500/3

â‡’(18x-35x)/6 = (5250 â€“ 9500)/3

â‡’-17x/6 = -4250/3

â‡’-17x = -8500

x = 500 â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦.. (IV)

Substituting the value of x in (III), we get

y = (3800-7 Ã—500)/6 = 300/6 = 50

Hence, the cost of a bat is Rs 500 and cost of a ball is Rs 50.

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