Question

Please help, find out q​

Answer 1

$\large\sf\underline{Question\::}$

• If N = $\sf\:\frac{m}{x+q}$ , find the value of q when N = $\sf\:1\frac{4}{5}$ , m = 9 and x = 2 .

‎

$\large\sf\underline{Answer\::}$

• The required value of q is $\small{\mathfrak{3}}$ .

==‎==================

$\large\bf\underline{Step~wise~calculation\::}$

$\small\sf\underline{Given\::}$

• N = $\sf\:1\frac{4}{5}$

• m = 9

• x = 2

‎

$\small\sf\underline{To\:find\::}$

• The value of q.

‎

$\small\sf\underline{Solution\::}$

Expression : $\sf\:N~=~\frac{m}{x+q}$

• Substituting the values of N , m and x as given

$\sf\implies\:1\frac{4}{5}~=~\frac{9}{2+q}$

• Converting the mixed fraction into improper fraction ( numerator is greater than denominator )

$\sf\implies\:\frac{9}{5}~=~\frac{9}{2+q}$

• Cross multiplying

$\sf\implies\: 9(2+q) =9 \times 5$

• Multiplying the numbers

$\sf\implies\: 18+9q =45$

• Transposing +18 to RHS it becomes -18

$\sf\implies\: 9q =45-18$

$\sf\implies\: 9q =27$

• Transposing 9 to RHS it goes to the denominator

$\sf\implies\: q =\frac{27}{9}$

• Reducing the fraction to lower terms

$\sf\implies\: q =\cancel{\frac{27}{9}}$

${\small{\underline{\boxed{\tt{\sf{\purple{\implies\:q=3}}}}}}}$ ★

‎

$\small\sf\underline{Verification\::}$

We got the value of q as 3 . Let's check if it is correct. In order to check we would plug the value of N, m, x and q all together in the given equation. Doing so and solving if we get LHS = RHS , our answers would be correct. Let's begin!

Expression : $\sf\:N~=~\frac{m}{x+q}$

• Substituting the values of the variables

$\sf\implies\:1\frac{4}{5}\:=\frac{9}{2+3}$

$\sf\implies\:\frac{9}{5}\:=\frac{9}{5}$

$\bf\implies\:LHS\:=\:RHS$

$\small\fbox\green{Hence~Verified~!! }$

________________________

$\dag\:\underline{\sf So\:the\:required\:value~of~q\:is\:3}$‎ .

‎

‎!! Hope it helps !!

Answer 2

Explanation:

‎

\large\sf\underline{Answer\::}

Answer:

The required value of q is \small{\mathfrak{3}}3 .

==‎==================

\large\bf\underline{Step~wise~calculation\::}

Step wise calculation:

\small\sf\underline{Given\::}

Given:

N = \sf\:1\frac{4}{5}1

5

4

m = 9

x = 2

‎

\small\sf\underline{To\:find\::}

Tofind:

The value of q.

‎

\small\sf\underline{Solution\::}

Solution:

Expression : \sf\:N~=~\frac{m}{x+q}N =

x+q

m

Substituting the values of N , m and x as given

\sf\implies\:1\frac{4}{5}~=~\frac{9}{2+q}⟹1

5

4

=

2+q

9

Converting the mixed fraction into improper fraction ( numerator is greater than denominator )

\sf\implies\:\frac{9}{5}~=~\frac{9}{2+q}⟹

5

9

=

2+q

9

Cross multiplying

\sf\implies\: 9(2+q) =9 \times 5⟹9(2+q)=9×5

Multiplying the numbers

\sf\implies\: 18+9q =45⟹18+9q=45

Transposing +18 to RHS it becomes -18

\sf\implies\: 9q =45-18⟹9q=45−18

\sf\implies\: 9q =27⟹9q=27

Transposing 9 to RHS it goes to the denominator

\sf\implies\: q =\frac{27}{9}⟹q=

9

27

Reducing the fraction to lower terms

\sf\implies\: q =\cancel{\frac{27}{9}}⟹q=

9

27

{\small{\underline{\boxed{\tt{\sf{\purple{\implies\:q=3}}}}}}}

⟹q=3

★

‎

\small\sf\underline{Verification\::}

Verification:

We got the value of q as 3 . Let's check if it is correct. In order to check we would plug the value of N, m, x and q all together in the given equation. Doing so and solving if we get LHS = RHS , our answers would be correct. Let's begin!

Expression : \sf\:N~=~\frac{m}{x+q}N =

x+q

m

Substituting the values of the variables

\sf\implies\:1\frac{4}{5}\:=\frac{9}{2+3}⟹1

5

4

=

2+3

9

\sf\implies\:\frac{9}{5}\:=\frac{9}{5}⟹

5

9

=

5

9

\bf\implies\:LHS\:=\:RHS⟹LHS=RHS

\small\fbox\green{Hence~Verified~!! }

Hence Verified !!