Question

Solve this question
$x + 930 = x \times 444 \frac{4}{9} \%$
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Answer 1

★ Concept :-

Here the concept of Linear Equation in one Variable and Percentage have been used. We see that we are given a equation which even has a percentage expression. Firstly we will solve that percentage expression and then take the x terms and solve them. After that we will keep on simplifying and thus find the value of x

Let's do it !!

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★ Solution :-

Given,

$\\\;\bf{\mapsto\;\;\red{x\;+\;930\;=\;x\:\times\:\bigg(444\dfrac{4}{9}\bigg)\%}}$

We shall solve this question step - by - step.

• Step I ::

In this step, firstly we will simplify the fraction at RHS. We see this, that the given fraction is a mixed fraction. We already know that method to solve it as,

$\\\;\tt{\leadsto\;\;a\dfrac{b}{c}\;=\;\dfrac{ac\:+\:b}{c}}$

We can apply this method in the given equation as,

$\\\;\sf{\rightarrow\;\;x\;+\;930\;=\;x\:\times\:\bigg(\dfrac{3996\:+\:4}{9}\bigg)\%}$

Since, 444 × 9 = 3996

$\\\;\bf{\rightarrow\;\;\orange{x\;+\;930\;=\;x\:\times\:\bigg(\dfrac{4000}{9}\bigg)\%}}$

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• Step II ::

In this step, we shall remove the percentage sign from RHS to make it a normal term like LHS. We already know that, when percentage sign is converted into normal term then we get,

$\\\;\tt{\leadsto\;\;a\%\;=\;\dfrac{a}{100}}$

Using this expression in the final equation of step I, we get

$\\\;\sf{\rightarrow\;\;x\;+\;930\;=\;\bf{x\:\times\:\bigg[\bigg(\dfrac{4000}{9}\bigg)\:\times\:\dfrac{1}{100}\bigg]}}$

$\\\;\displaystyle{\sf{\rightarrow\;\;x\;+\;930\;=\;\bf{x\:\times\:\bigg[\dfrac{\bigg(\frac{4000}{9}\bigg)}{100}\bigg]}}}$

$\\\;\displaystyle{\sf{\rightarrow\;\;x\;+\;930\;=\;\bf{x\:\times\:\bigg[\dfrac{\frac{4000}{9}}{100}\bigg]}}}$

$\\\;\sf{\rightarrow\;\;x\;+\;930\;=\;\bf{x\:\times\:\bigg[\dfrac{4000}{900}\bigg]}}$

Cancelling the fraction at RHS by 100, we get

$\\\;\bf{\rightarrow\;\;\blue{x\;+\;930\;=\;x\:\times\:\bigg[\dfrac{40}{9}\bigg]}}$

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• Step III ::

In this step, we will take the common terms at different sides that is variable term at LHS and constant terms at RHS.

Constant terms are those which have no unknown quantities. Variable terms are those which have unknown quantities like x.

In order to simplify it, we shall take the final equation of Step II.

$\\\;\sf{\rightarrow\;\;x\;+\;930\;=\;\bf{x\:\times\:\bigg[\dfrac{40}{9}\bigg]}}$

$\\\;\sf{\rightarrow\;\;x\;+\;930\;=\;\bf{x\:\times\:\dfrac{40}{9}}}$

$\\\;\sf{\rightarrow\;\;x\;+\;930\;=\;\bf{\dfrac{40x}{9}}}$

$\\\;\sf{\rightarrow\;\;\;930\;=\;\bf{\dfrac{40x}{9}\;-\;x}}$

$\\\;\sf{\rightarrow\;\;\dfrac{40x}{9}\;-\;x\;=\;\bf{930}}$

Taking the LCM, we get

$\\\;\sf{\rightarrow\;\;\dfrac{40x\;-\;9x}{9}\;=\;\bf{930}}$

$\\\;\sf{\rightarrow\;\;\dfrac{31x}{9}\;=\;\bf{930}}$

$\\\;\sf{\rightarrow\;\;\dfrac{31x}{9}\;=\;\bf{\dfrac{930}{1}}}$

Since a/1 = a

$\\\;\sf{\rightarrow\;\;31x\:\times\:1\;=\;\bf{930\:\times\:9}}$

$\\\;\sf{\rightarrow\;\;31x\;=\;\bf{930\:\times\:9}}$

$\\\;\bf{\rightarrow\;\;\green{31x\;=\;\bf{8370}}}$

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• Step IV ::

In this step, we shall find the value of x. We see that we have a got a clear Linear Equation in One Variable from a complex sentence given. Now equating, we get

$\\\;\sf{\Longrightarrow\;\;31x\;=\;\bf{8370}}$

Now dividing both sides that is LHS and RHS by 31 , we get

$\\\;\sf{\Longrightarrow\;\;\dfrac{31x}{31}\;=\;\bf{\dfrac{8370}{31}}}$

Since dividing at both sides by same term, won't let the initial value of equation change. So,

$\\\;\sf{\Longrightarrow\;\;x\;=\;\bf{\dfrac{8370}{31}}}$

$\\\;\sf{\Longrightarrow\;\;x\;=\;\bf{270}}$

Hence we got the value of x as 270

$\\\;\underline{\boxed{\tt{Hence,\;\:value\;\:of\;\:x\;=\;\bf{\purple{270}}}}}$

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★ Verification :-

For verification of the value of x that if we got the value of x as correct or not, then we have to apply the value of x that we got from above in the initial equation.

$\\\;\tt{\rightarrow\;\;x\;+\;930\;=\;x\:\times\:\bigg[\dfrac{40}{9}\bigg]}$

Since, x = 270

$\\\;\tt{\rightarrow\;\;270\;+\;930\;=\;270\:\times\:\bigg[\dfrac{40}{9}\bigg]}$

$\\\;\tt{\rightarrow\;\;270\;+\;930\;=\;270\:\times\:\dfrac{40}{9}}$

$\\\;\tt{\rightarrow\;\;1200\;=\;30\:\times\:40}$

$\\\;\bf{\rightarrow\;\;1200\;=\;1200}$

Clearly, LHS = RHS. Since the equation satisfies by the value of x, so our answer is correct.

Hence, Verified !!

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★ More to know :-

• Linear Equations : These are the equations formed using constant and variable terms where we need to usually find the value of the unknown term.

Types of Linear Equations ::

• Linear Equations in One Variable

• Linear Equations in Two Variables

Answer 2

Answer:

x + 930 = x × 444(4/9)%

x + 930 = x × (4000/9)%

x + 930 = x × 4000/9*100

x + 930 = x × 40/9

x + 930 = 40x/9

9(x + 930) = 40x

9x + 8370 = 40x

8370 = 40x - 9x

8370 = 31x

31x = 8370

x = 8370/31

x = 270