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In a class test, the sum of Shefali’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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Let Mathematics marks be x and that of English be y, Solve the following equations: x+y=30____(i) (x+2)(y-3)=210___(ii) In equtation (ii) substitute y in terms of x using equation (i), then we get (x+2)(27-x)=210 solving the above quadration equation two possible... read more

Let Mathematics marks be x and that of English be y,

Solve the following equations: x+y=30____(i)

(x+2)(y-3)=210___(ii)

In equtation (ii) substitute y in terms of x using equation (i), then we get (x+2)(27-x)=210

solving the above quadration equation two possible values(marks) of x(mathematics) exists.

At x=12, y=18 & at x=13, y=17

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Let x and y be the marks of Shefali in Mathematics and English. Now Sum of the marks are 30, i.e., x + y = 30 Again, (x+2)(y-3) = 210 =>xy - 3x + 2y - 6 = 210 =>x(30 -x) - 3x +2(30 - x) = 216 =>30x - x^2 - 3x + 60 - 2x = 216 =>25x - x^2 - 156 = 0 =>x^2 - 25x + 156 = 0 => x =... read more

Let x and y be the marks of Shefali in Mathematics and English. Now

Sum of the marks are 30, i.e., x + y = 30

Again, (x+2)(y-3) = 210 =>xy - 3x + 2y - 6 = 210 =>x(30 -x) - 3x +2(30 - x) = 216

=>30x - x^2 - 3x + 60 - 2x = 216

=>25x - x^2 - 156 = 0

=>x^2 - 25x + 156 = 0

=> x = (25+1)2 = 13 or 12

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Let the marks in Maths be x so the marks in English = (30 - x). ATQ, (x + 2) (27 - x) = 210 or 27x - x² + 54 - 2x = 0 or - x² + 25x - 156 = 0 or x² - 25x + 156 = 0 or x² - 13x - 12x + 156 = 0 or x(x - 13) - 12(x - 13) = 0 or (x - 12) (x - 13) = 0 Therefore, x = 12 or x = 13 Hence,... read more

Let the marks in Maths be x so the marks in English = (30 - x).

ATQ, (x + 2) (27 - x) = 210

or 27x - x² + 54 - 2x = 0

or - x² + 25x - 156 = 0

or x² - 25x + 156 = 0

or x² - 13x - 12x + 156 = 0

or x(x - 13) - 12(x - 13) = 0

or (x - 12) (x - 13) = 0

Therefore, x = 12 or x = 13

Hence, marks in Maths is 12 or 13, therefore, marks in English is either 17 or 18.

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