Question

denominator of rational number that is greater than it's numerator by 7.if the numerator is increased by 17 and the denominator is decreased by 6 ,the new number becomes 2 find the area of the plate​

Answer 1

Appropriate Question :

• The denominator of rational number that is greater than it's numerator by 7.if the numerator is increased by 17 and the denominator is decreased by 6 ,the new number becomes 2. find the original number .

Given :

• The denominator of rational number that is greater than it's numerator by 7.
• if the numerator is increased by 17 and the denominator is decreased by 6,the new number becomes 2.

To Find :

• The original number = ?

Solution :

• Let numerator be a and then denominator will be a + 7.

If the numerator is increased by 17,mathematically it can be expressed as :

• a + 17

And the denominator is decreased by 6,mathematically it can be expressed as :

• a + 7 - 6

★ According to Question now :

→ Numerator ÷ Denomintaor = 2

→ (a + 17) ÷ (a + 7 - 6) = 2

→ (a + 17) ÷ (a + 1) = 2

→ a + 17 = 2(a + 1)

→ a + 17 = 2a + 2

→ 17 - 2 = 2a - a

→ 15 = a

→ a = 15

• Hence,the numerator of the given number is 15.

★ Finding the denomintaor :

→ Denomintaor = a + 7

→ Denomintaor = 15 + 7

→ Denominator = 22

• Hence,the denomintaor of the given number is 22.

★ Finding the original number :

→ Original Number = Denomintaor ÷ Numerator

→ Original Number = a ÷ (a + 7)

→ Original Number = 15/22

• Hence,the original number is 15/22.

Answer 2

$\huge{\boxed{\bold{Question}}}$

denominator of rational number that is greater than it's numerator by 7.if the numerator is increased by 17 and the denominator is decreased by 6 ,the new number becomes 2 find the area of the plate

${ \boxed { \boxed{ \boxed{ \rm \: answer}}}} \\ \\ \sf \rightarrow let \: us \: take \: the \: numerator \: to \: be \: x \\ \\ \rightarrow \sf \: so \: the \: denominator \: \: will \: be \: x + 7 \\ \\ \boxed{ \tt \: given \: codition \: is ? } \\ \\ \implies \rm \: the \: numerator \: when \: increased \: by \: 17 = x + 17 \\ \implies \rm \: and \: the \: denominator \: when \: decresed \: by \\ \\ \longmapsto \: \tt \: 6 = x + 7 - 7 \\ \longmapsto \tt \: x + z \\ \\ \sf \: then \: thus \: must \: be \: equal \: to \: 2 \\ \\ \longmapsto\boxed{ \frac{ \tt \: x + 17}{ \tt \: x + 1} } \\ \\ \leadsto \tt \: (x + 17) = 2(x + 1) \\ \\ \leadsto \tt \: x + 17 = 2x + 2 \\ \\ \leadsto \tt \: 2x - x = 17 - 2 \\ \\ { \boxed { \boxed{ \boxed{ \boxed{ \boxed{ \mathfrak{x = 15 /22\: answer}}}}}}}$