the numerator of a rational is less than its denominater by 4 .if the

1.	the numerator of a rational is less than its denominater by 4 .if the numerator is multiplied by 2 and the denominator is increased by 4 the number becomes 14/15. find the origanal number.
Answer» Answer:- Let the NUMBER be x/y. Given: NUMERATOR is less than the denominator by 4. ⟶ Numerator = Denominator - 4 ⟶ x = y - 4 -- equation (1) And, If the numerator is MULTIPLIED by 2 and denominator is increased by 4 , the number becomes 14/15. $\longrightarrow \sf \dfrac{2 \times x}{y + 4} = \dfrac{14}{15}$ SUBSTITUTE the value of x from equation (1). $\: \longrightarrow \sf \: \frac{2(y - 4)}{y + 4} = \frac{14}{15} \\ \\ \longrightarrow \sf \: \frac{2y - 8}{y + 4} = \frac{14}{15} \\ \\ \longrightarrow \sf \: 15(2y - 8) = 14(y + 4) \\ \\ \longrightarrow \sf \: 30y - 120 = 14y + 56 \\ \\ \longrightarrow \sf \: 30y - 14y = 56 + 120 \\ \\ \longrightarrow \sf \: 16y = 176 \\ \\ \longrightarrow \sf \: y = \frac{176}{16} \\ \\ \longrightarrow \boxed{ \sf \: y = <klux>11</klux>}$ Substitute the value of y in equation (1). ⟶ x = y - 4 ⟶ x = 11 - 4 ⟶ x = 7 ∴ The required number x/y is 7/11.

the numerator of a rational is less than its denominater by 4 .if the numerator is multiplied by 2 and the denominator is increased by 4 the number becomes 14/15. find the origanal number.

Answer»

Answer:-

Let the NUMBER be x/y.

Given:

NUMERATOR is less than the denominator by 4.

⟶ Numerator = Denominator - 4

⟶ x = y - 4 -- equation (1)

And,

If the numerator is MULTIPLIED by 2 and denominator is increased by 4 , the number becomes 14/15.

$\longrightarrow \sf \dfrac{2 \times x}{y + 4} = \dfrac{14}{15}$

SUBSTITUTE the value of x from equation (1).

$\: \longrightarrow \sf \: \frac{2(y - 4)}{y + 4} = \frac{14}{15} \\ \\ \longrightarrow \sf \: \frac{2y - 8}{y + 4} = \frac{14}{15} \\ \\ \longrightarrow \sf \: 15(2y - 8) = 14(y + 4) \\ \\ \longrightarrow \sf \: 30y - 120 = 14y + 56 \\ \\ \longrightarrow \sf \: 30y - 14y = 56 + 120 \\ \\ \longrightarrow \sf \: 16y = 176 \\ \\ \longrightarrow \sf \: y = \frac{176}{16} \\ \\ \longrightarrow \boxed{ \sf \: y = <klux>11</klux>}$

Substitute the value of y in equation (1).

⟶ x = y - 4

⟶ x = 11 - 4

⟶ x = 7

∴ The required number x/y is 7/11.