Question

The numerator of a fraction is 3 less than its denominator. If 2 is added to both of its numerator and denominator then the sum of the new fraction and original is 29/20. find the original fraction.

(Plzz assume numerator = x
and denominator = y) ​

Answer 1

$\color {red}\huge\bold\star\underline\mathcal{Question:-}$ we have to find original Fraction ..

$\huge\underline\blue{\sf Given:}$

Numerator is 3 less than denominator ..

$\rule{200}{4}$

$\bold{\boxed{\huge{\boxed{\orange{\small{\boxed{\huge{\red{\bold{\:Answer}}}}}}}}}}$

Let Numerator = x

Denominator = y

so,

A/q,

$y - x = 3 - - - - (equation1)$

Now,

$\frac{x}{y} + ( \frac{x + 2}{y + 2} ) = \frac{29}{20} \\ \\ \frac{xy + 2x + xy + 2y}{y(y + 2)} = \frac{29}{20}$

$40xy + 40x + 40y = 29y^{2} + 58y \\ \\ 29y ^{2} + 58y - 40xy - 40x - 40y = 0$

Putting value of y = (x+3) now ,

$29(x + 3)^{2} + 58x + 174 - 40 {x}^{2} - 00x - 120 = 0 \\ \\ 11x ^{2} - 32x - 315 = 0 \\ \\ 11 {x}^{2} - 77x + 45x - 315 = 0 \\ \\ 11x(x - 7) + 45(x - 7) = 0 \\ \\ (11x + 45)(x - 7) = 0 \\ \\ x = \frac{ - 45}{11} \: or \: 7$

so,

$y = 7 + 3 = 10$

$\</strong><strong>h</strong><strong>u</strong><strong>g</strong><strong>e</strong><strong>\red{\boxed{\sf </strong><strong> </strong><strong>Fraction\</strong><strong>:</strong><strong>=</strong><strong>\</strong><strong>:</strong><strong>\frac{7}{10}</strong><strong>}}$

Answer 2

Answer:

answer in the picture format..

hope you get it...