Question

The denominator of rational number is greater than its numerator by 7. If the numerator is increased by 17 and the denominator is decreased by 8 the number obtained is 5/3 Find the rational number

Step by step explanation ​

Answer 1

Answer:

it's your answer

Step-by-step explanation:

Mark me brainleist answer

Answer 2

Answer:

28/35

Step-by-step explanation:

As per the provided information in the given question, we have :

• The denominator of rational number is greater than its numerator by 7.
• If the numerator is increased by 17 and the denominator is decreased by 8 the number obtained is 5/3.

We are asked to calculate the rational number.

Let the numerator of the rational number be x. And, the denominator of the rational number be y.

― According to the given question, the denominator of rational number is greater than its numerator by 7. Writing this statement in the form of a linear equation,

$\longrightarrow \sf{\quad {y = x + 7 \dots (1) }}$

Also, in the question it has been stated that if the numerator is increased by 17 and the denominator is decreased by 8 the number obtained is 5/3.

$\longrightarrow \sf{\quad { \Bigg \{ \dfrac{x + 17}{y - 8} \Bigg \}= \dfrac{5}{3}}}$

Substitute the value of y in the terms of x from the equation ( 1 ).

$\longrightarrow \sf{\quad { \Bigg \{ \dfrac{x + 17}{(x + 7) - 8} \Bigg \}= \dfrac{5}{3}}}$

Remove the brackets.

$\longrightarrow \sf{\quad { \Bigg \{ \dfrac{x + 17}{x + 7 - 8} \Bigg \}= \dfrac{5}{3}}}$

Performing subtraction in the the denominator of the LHS.

$\longrightarrow \sf{\quad { \dfrac{x + 17}{x - 1} = \dfrac{5}{3}}}$

Now, using the cross multiplication method and cross multiplying the values.

$\longrightarrow \sf{\quad { 3(x + 17) = 5(x - 1) }}$

Performing multiplication in both LHS ans RHS.

$\longrightarrow \sf{\quad { 3x + 51 = 5x - 5}}$

Transposing the like terms. Their signs will get changed.

$\longrightarrow \sf{\quad { 51 +5 = 5x - 3x}}$

Performing addition in LHS and subtraction in RHS.

$\longrightarrow \sf{\quad { 56 = 2x}}$

Transposing 2 from RHS to LHS.

$\longrightarrow \sf{\quad { \cancel{\dfrac{56}{2}} = x}}$

Dividing 56 by 2.

$\longrightarrow {\quad {\textbf{\textsf{ 28 = x }}}}$

― Now, we have to find the value of y too. So, substitute the value of x in the equation (1) to calculate the value of y.

Equation 1 :

$\longrightarrow \sf{\quad {y = x + 7 }}$

Substitute the value of x.

$\longrightarrow \sf{\quad {y = 28 + 7 }}$

Performing addition.

$\longrightarrow {\quad {\textbf{\textsf{ y = 35 }}}}$

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

Henceforth,

$\longrightarrow \sf{\quad {Number = \dfrac{Numerator \; (x)}{Denominator \; (y)} }}$

Substitute the values.

$\longrightarrow \quad \underline {\boxed{\textbf{\textsf{ Number }} = \dfrac{\textbf{\textsf{28 }}}{\textbf{\textsf{35 }}} } }$