Question

What number must be added to each term of the ratio 9:16 to make the ratio 2:3?(With proper solution i will make it as brainleist)​

Answer 1

Answer:

• 5 must be added to each term of the ratio 9 : 16 to make the ratio 2 : 3.

Step-by-step explanation:

To Find:

• What number must be added to each term of the ratio 9 : 16 to make the ratio 2 : 3?

Let us assume:

• x must be added to each term of the ratio 9 : 16 to make the ratio 2 : 3.

Finding the value of x:

According to the question.

⟶ (9 + x)/(16 + x) = 2/3

Cross multiplication.

⟶ 3(9 + x) = 2(16 + x)

⟶ 27 + 3x = 32 + 2x

⟶ 3x - 2x = 32 - 27

⟶ x = 5

Hence,

• 5 must be added to each term of the ratio 9 : 16 to make the ratio 2 : 3.

Answer 2

Given : The number must be added to each term of the ratio 9:16 to make the ratio 2:3 .

Need To Find : The number which is added to each term of the ratio 9:16 to make the ratio 2:3 .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's Consider the number be a which must be added to each term of ratio 9:16 to make the ratio 2:3.

Now ,

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\: \: According \: to \: the \: Question \::}}$

⠀⠀⠀⠀⠀━━━ a must be added to each term of the ratio 9:16 to make the ratio 2:3 .

$\qquad \dashrightarrow \sf \dfrac{9 + a }{16 + a } \:\:=\: \dfrac{2}{3}$

$\qquad \dashrightarrow \sf 3 ( 9 + a )\:=\: 2 ( 16 + a ) \:\:$

$\qquad \dashrightarrow \sf 27 + 3a \:=\: 2 ( 16 + a ) \:\:$

$\qquad \dashrightarrow \sf 27 + 3a \:=\: 32 + 2a \:\:$

$\qquad \dashrightarrow \sf 27 + 3a - 2a \:=\: 32 \:\:$

$\qquad \dashrightarrow \sf 27 + a \:=\: 32 \:\:$

$\qquad \dashrightarrow \sf a \:=\: 32 - 27 \:\:$

$\qquad \dashrightarrow \sf a \:=\: 5 \:\:$

$\qquad \therefore \pmb{\underline{\purple{\:a \: = 5 }} }\:\:\bigstar$

• Here , a signifies the number that must be added which is 5

$\qquad \therefore \underline { \sf Hence , \: \bf 5 \: \sf must \: be \: added \:to \: each \: term \:of \: ratio\: 9:16 \:to \:make \:the \:ratio \:2:3 \:.\:}$