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In a class test, the sum of Neha's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.?
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In a class test, the sum of Neha's marks in Mathematics and English is...
To solve the problem of Neha's marks in Mathematics and English, we need to establish a system of equations based on the information provided.
Step 1: Establish the Equations
Let:
- Neha's marks in Mathematics = x
- Neha's marks in English = y
From the problem, we have two pieces of information:
1. The sum of her marks in Mathematics and English is 30:
- x + y = 30
2. If she had 2 more marks in Mathematics and 3 less in English, the product of their marks would be 210:
- (x + 2)(y - 3) = 210
Step 2: Substitute and Rearrange
From the first equation, we can express y in terms of x:
- y = 30 - x
Now, substitute this value into the second equation:
- (x + 2)((30 - x) - 3) = 210
- (x + 2)(27 - x) = 210
Step 3: Expand and Simplify
Expanding the equation:
- x * 27 - x^2 + 54 - 2x = 210
- -x^2 + 25x + 54 - 210 = 0
- -x^2 + 25x - 156 = 0
Multiplying through by -1 to simplify:
- x^2 - 25x + 156 = 0
Step 4: Solve the Quadratic Equation
Using the quadratic formula:
- x = [25 ± √(25² - 4*1*156)] / 2
- x = [25 ± √(625 - 624)] / 2
- x = [25 ± 1] / 2
Thus, we get:
- x = 13 (Mathematics)
- x = 12 (English)
Final Result:
- Neha's marks in Mathematics = 13
- Neha's marks in English = 17
Step 1: Establish the Equations
Let:
- Neha's marks in Mathematics = x
- Neha's marks in English = y
From the problem, we have two pieces of information:
1. The sum of her marks in Mathematics and English is 30:
- x + y = 30
2. If she had 2 more marks in Mathematics and 3 less in English, the product of their marks would be 210:
- (x + 2)(y - 3) = 210
Step 2: Substitute and Rearrange
From the first equation, we can express y in terms of x:
- y = 30 - x
Now, substitute this value into the second equation:
- (x + 2)((30 - x) - 3) = 210
- (x + 2)(27 - x) = 210
Step 3: Expand and Simplify
Expanding the equation:
- x * 27 - x^2 + 54 - 2x = 210
- -x^2 + 25x + 54 - 210 = 0
- -x^2 + 25x - 156 = 0
Multiplying through by -1 to simplify:
- x^2 - 25x + 156 = 0
Step 4: Solve the Quadratic Equation
Using the quadratic formula:
- x = [25 ± √(25² - 4*1*156)] / 2
- x = [25 ± √(625 - 624)] / 2
- x = [25 ± 1] / 2
Thus, we get:
- x = 13 (Mathematics)
- x = 12 (English)
Final Result:
- Neha's marks in Mathematics = 13
- Neha's marks in English = 17
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In a class test, the sum of Neha's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.?
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In a class test, the sum of Neha's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.? 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 In a class test, the sum of Neha's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class test, the sum of Neha's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.?.
In a class test, the sum of Neha's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.? 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 In a class test, the sum of Neha's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class test, the sum of Neha's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.?.
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