Question

had dhwani scored 10 more marks in her mathematics test out of 30 marks 9 time this marks would have been the square of actual marks how many marks did she got test
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Answer 1

The Total Marks she scored in her mathematics test is 15 out of 30.

Step-by-step explanation:

Let actual marks she got be 'x'.

Now given:

If Dhwani scored 10 more marks in her mathematics test out of 30 marks 9 time this marks would have been the square of actual marks.

It means that 9 times sum of actual marks she scored and 10 is equal to square of the actual mars she score.

framing in equation form we get;

$9(x+10) = x^2$

Now By Using Distributive property we get;

$9x+90=x^2\\\\x^2-9x+90 = 0$

Now Using factorization form to find the roots of 'x' we get;

$x^2-15x+6x-90=0\\\\x(x-15)+6(x-15)=0\\\\(x+6)(x-15)=0$

Now  we will solve for 2 values we get;

$x+6 = 0\\\\x = -6\\\\OR\\\\x-15=0\\\\x =15$

Since the marks she scored cannot be negative.

So we will neglect $x= -6$

Hence The Total Marks she scored in her mathematics test is 15 out of 30.

Verifying the same we get;

$9(x+10) = x^2\\\\9(15+10)=15^2\\\\9\times 25 = 225\\\\225 =225$