Question

The coach of a cricket team buys 7 bats and 6 balls for 13200. Later he buys 3 bats and 5 balls for 5900. find the cost of each bat and each ball.

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Answer 1

Explanation:

$\bf \red{✬ Ball = Rs 100 ✬}$

$\bf \red{✬ Bat = Rs 1800 ✬}$

Given:

• Cost of 7 bats and 6 balls is Rs 13200.
• Cost of 3 bats and 5 balls is Rs 5900.

To Find:

What is the cost of each bat and ball ?

Solution:

• Let the cost of each bat and ball be Rs x and y respectively.

➙ Cost of 7 bats = Rs 7x

➙ Cost of 6 balls = Rs 6y

$\implies{\rm }7x + 6y = 13200$

Equation 1

$\bf \purple{Now , In \: second \: case}$

➙ Cost of 3 bats = Rs 3x

➙ Cost of 5 balls = Rs 5y

$\implies{\rm }3x + 5y = 5900$

Equation 2

[ Multiplying 5 in equation 1 and 6 in equation 2 ]

➯ (7x + 6y) 5 = 13200 × 5

35x + 30y = 66000ㅤㅤㅤeqⁿ i

➯ (3x + 5y) 6 = 5900 × 6

18x + 30y = 35400ㅤㅤeqⁿ ii

ㅤㅤㅤㅤㅤ35x + 30y = 66000

ㅤㅤㅤㅤㅤ18x + 30y = 35400

ㅤㅤㅤㅤㅤ–ㅤㅤ–ㅤㅤ–

ㅤㅤㅤㅤ━━━━━━━━━━━━━━━

$\bf \blue{ㅤㅤㅤㅤㅤ17x = 30600}$

$\sf \red{∴ x = 30600/17 = 1800}$

Now putting the value of x in equation 1.

$\implies{\rm } 7 × 1800 + 6y = 13200$

$\implies{\rm } 6y = 13200 – 12600$

$\implies{\rm } y = 600/6$

$\implies{\rm }y = 100$

Hence, the cost of each bat and ball is Rs 1800 & Rs 100 respectively.

_____________________

Answer 2

Explanation:

Given :-

The coach of a cricket team buys 7 bats and 6 balls for 13200. Later he buys 3 bats and 5 balls for 5900

To Find :-

Cost of one bat and ball

Solution :-

Let

Price of bat = x

Price of ball = y

Now

7 × x + 6 × y = 13200

7x + 6y = 13200

Multiply by 5

5(7x + 6y) = 5(13200)

35x + 30y = 66000(1)

Now

3 × x + 5 × y = 5900

3x + 5y = 5900

Multiply by 6

6(3x + 5y) = 6(5900)

18x + 30y = 35400

Subtracting them

(35x + 30y) - (18x + 30y) = 66000 - 35400

35x + 30y - 18x - 30y = 30600

35x - 18x = 30600

17x = 30600

x = 30600/17

x = 1800

By putting in 1

35(1800) + 30y = 66000

63000 + 30y = 66000

30y = 66000 - 63000

30y = 3000

y = 3000/30

y = 100

$\begin{gathered}\\\end{gathered}$