Think you can solve this problem ?

Question

O beautiful maiden with beaming eyes,tel me,since you understand the method of inversion,what number multiplied by 3 ,then increaed by 3/4 of the product,then divided by 7,the diminished by 1/3 of the reslt,then multiplied by itself,then diminished by 52,whose square root is then extracted before 8 is added and then divided by 10 gives the final result of ?

I found this riddle in the Book; Introducting Mathematics by Icon books. It's supposed to be an Indian riddle froom India. The answer is 28.

Answer 1

The question is, using "x" for the number that you start with, and "y" for the number that results:

{ sqrt( [ ( (3*x) * (1 + 3/4) / 7 ) * 2/3 ]^2 - 52 ) + 8 } / 10 = y

Solving for y and combining terms that can be combined:

y = { sqrt( [ ( (3*x) * (1 + 3/4) / 7 ) * 2/3 ]^2 - 52 ) + 8 } / 10
10y = sqrt( [ ( (3*x) * (1 + 3/4) / 7 ) * 2/3 ]^2 - 52 ) + 8
10y - 8 = sqrt( [ ( (3*x) * (7/4) / 7 ) * 2/3 ]^2 - 52 )
(10y - 8)^2 = [ ( (3*x) * (1/4) ) * 2/3 ]^2 - 52
(10y - 8)^2 + 52 = [ ( x * (1/4) ) * 2 ]^2
sqrt((10y - 8)^2 + 52) = x/2
2 * sqrt((10y - 8)^2 + 52) = x

The answer depends on what you mean by "?". If there is a specific value, you can plug it into that equation. If you want to know what number(s) emerge unchanged from that set of operations, you'd want to solve this equation, assuming y=x:
(10y - 8)^2 + 52 = [ ( x * (1/4) ) * 2 ]^2

Answer 2

Thanks for the flattery. To solve this, just let "x" equal the unknown number and do the computations they ask for.

3x + (3/4)(3x) = 12x/4 + 9x/4 = 21x/4

(21x/4) / 7 = 3x/4

3x/4 - (1/3)3x/4 = (2/3)3x/4 = 2x/4 = x/2

(x/2)(x/2) = (x^2)/4

√[(x^2)/4 - 52] + 8

[ √[(x^2)/4 - 52] + 8 ] / 10

You don't say what this is the final result of. Let's call it "R" for result. Then the original number, in terms of the result, is:

[ √[(x^2)/4 - 52] + 8 ] / 10 = R
√[(x^2)/4 - 52] + 8 = 10R
√[(x^2)/4 - 52] = 10R - 8
(x^2)/4 - 52 = (10R - 8)^2
(x^2)/4 = 52 + (10R - 8)^2
(x^2) = 208 + (10R - 8)^2
x = √ [208 + (10R - 8)^2]

Answer 3

Note that the result should be mentioned at the end of the problem and it is '2'. That should help out ppl who are trying to solve it.

Answer 4

i'm not a maiden but its 29......................................