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The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically.?
Most Upvoted Answer
The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later,...
let the price of 1bat=x and price of one ball=y
case1:
3x+6y=3900
( dividing both sides by 3)
x+2y=1300--(1)
case2:
x+3y=1300--(2)
putting x=0 in(1)
3y=1300
y=650
algebraically solution for equation 1=(0, 650)
putting x=100 in (1)
2y=1200
y=600
x y
0 650
100 600
For eq(2)
by putting x=0
we get y=433.3
by putting x=100
we get y=400
x y
0 433.3
100 400
Graphically:
Community Answer
The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later,...
Algebraic representation:
Let the cost of one bat and one ball be x and y respectively.
Then, as per the given information,
3x + 6y = 3900 ...(1)
And,
1x + 3y = 1300 ...(2)
Geometric representation:
The given information can be represented geometrically as follows:
Consider a 2D plane, where x-axis represents the cost of one bat and y-axis represents the cost of one ball.
Then, equation (1) represents a line passing through the points (0,650) and (1300,0) on the plane.
Similarly, equation (2) represents a line passing through the points (0,433.33) and (1300,0) on the plane.
The solution to this system of equations (1) and (2) represents the point of intersection of these two lines, which gives the cost of one bat and one ball.
Solution:
Multiplying equation (2) by 2, we get:
2x + 6y = 2600
Subtracting this equation from equation (1), we get:
x = 1300
Substituting this value of x in equation (2), we get:
3y = 650
Thus, y = 216.67
Hence, the cost of one bat is ₹ 1300 and the cost of one ball is ₹ 216.67.
We can verify that these values satisfy both equations (1) and (2).
Conclusion:
The algebraic and geometric representations help us to solve the given problem in an organized and systematic way, which makes it easier to understand and interpret the solution.
Let the cost of one bat and one ball be x and y respectively.
Then, as per the given information,
3x + 6y = 3900 ...(1)
And,
1x + 3y = 1300 ...(2)
Geometric representation:
The given information can be represented geometrically as follows:
Consider a 2D plane, where x-axis represents the cost of one bat and y-axis represents the cost of one ball.
Then, equation (1) represents a line passing through the points (0,650) and (1300,0) on the plane.
Similarly, equation (2) represents a line passing through the points (0,433.33) and (1300,0) on the plane.
The solution to this system of equations (1) and (2) represents the point of intersection of these two lines, which gives the cost of one bat and one ball.
Solution:
Multiplying equation (2) by 2, we get:
2x + 6y = 2600
Subtracting this equation from equation (1), we get:
x = 1300
Substituting this value of x in equation (2), we get:
3y = 650
Thus, y = 216.67
Hence, the cost of one bat is ₹ 1300 and the cost of one ball is ₹ 216.67.
We can verify that these values satisfy both equations (1) and (2).
Conclusion:
The algebraic and geometric representations help us to solve the given problem in an organized and systematic way, which makes it easier to understand and interpret the solution.
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The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically.?
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The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically.?.
The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically.?.
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