Question

When x is added to each term of 7:13 the ratio becomes 2:3. The value of x is

Answer 1

QuEsTiOn:-

▪ When x is added to each term of 7 : 13 , the ratio becomes 2:3 . The value of x is....

SoLuTiOn:-

${ \blue{ \bold{ \underline{given}}}}$

▪ on adding x to the ratio 7 : 13 , it becomes 2:3

${ \blue{ \bold{ \underline{to \: find}}}}$

▪ The value of x ????

• original ratio = 7 : 13

• new ratio = 2 : 3

${ \pink{ \bold{ \underline{according \: to \: the \: question}}}}$

${ \red{ \bold{ \frac{(7 + x)}{(13 + x)} = \frac{2}{3} }}}$

▪ cross multiplying both side....

${ \bold{ \implies{3(7 + x) = 2(13 + x)}}}$

${ \bold{ \implies{21 + 3x = 26 + 2x}}}$

${ \bold{ \implies{3x - 2x = 26 - 21}}}$

${ \underline{ \huge{ \boxed{ \bold{ \implies{ \red{x = 5 \: \: }}}}}}}$

thus,

when 5 is added to each term of the ratio 7 : 13 , the ratio becomes 2 : 3

Answer 2

$\huge\underline\mathtt\blue{Question:}$

When x is added to each term of 7:13 the ratio becomes 2:3. The value of x is?

$\underline\orange{\boxed{\mathtt{\color{pink}{Given:}}}}$

$\mathtt\red{By \: adding \: x \: to \: the \: ratio \: 7:13}$$\mathtt\red{then, \: it \: becomes \: 2:3}$

$\underline\orange{\boxed{\mathtt{\color{pink}{To~Find:}}}}$

$\mathtt\green{The \: value \: of \: x = ?}$

$\underline\orange{\boxed{\mathtt{\color{pink}{Solution:}}}}$

$\mathtt\orange{By \: condition}$

$\sf\color{teal}\frac{7 + x}{13 + x} = \frac{2}{3}$

$\mathtt\color{indigo}Now, \: by \: cross \: multiplying \: in \\ \mathtt\color{indigo}both \: sides \: we \: get$

$\sf\pink{\implies 21 + 3x = 26 + 2x}$

$\sf\pink{\implies 3x - 2x = 26 - 21}$

${\boxed{\sf{\pink{\implies x = 5 }}}}$

$\mathtt\color{lawngreen}Hence \: the \: value \: of \: x \: = 5$