Question

6 was multiplied by a particular number. Then, 76.2 was divided into the product. Finally,
11.2 was added to this quotient, giving 12.2. State the initial number.

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large{\green{\underline \bold{\tt{Given :-}}}}$

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• 6 was multiplied by a particular number

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• Then, 76.2 was divided from the product.

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• Then,11.2 was added to this quotient

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• The final results is 12.2

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$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

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• The initial number

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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• Let the initial number be "x"

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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6 was multiplied by a particular number

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$\underline{\bold{\texttt{So the resultant will be :}}}$

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➠ 6x

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Then, 76.2 was divided from the product

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$\underline{\bold{\texttt{So the resultant will be :}}}$

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➠ [(6x) ÷ 76.2]

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Then,11.2 was added to the quotient

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$\underline{\bold{\texttt{So the resultant will be :}}}$

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➠ [(6x) ÷ 76.2] + 11.2

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Given that the final number is 12.2

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$\underline{\bold{\texttt{So the equation will be :}}}$

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➜ [(6x) ÷ 76.2] + 11.2 = 12.2

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➜ [(6x) ÷ 76.2] = 12.2 - 11.2

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➜ [(6x) ÷ 76.2] = 1

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So,

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➜ $\sf \dfrac { 6x } { 76.2 } = 1$

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⟮ Multiplying the above equation by 76.2 ⟯

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➜ $\sf \dfrac { 6x } { 76.2 } \times 76.2 = 1 \times 76.2$

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➜ $\sf \dfrac { 6x } { 1 } = 76.2$

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➜ 6x = 76.2

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➜ $\sf x = \dfrac { 76.2 } { 6 }$

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➨ x = 12.7

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• Hence the initial number was 12.7

Answer 2

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let the initial number be "x"

$\:\:$

$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

6 was multiplied by a particular number

$\:\:$

$\underline{\bold{\texttt{So the resultant will be :}}}$

$\:\:$

➠ 6x

$\:\:$

Then, 76.2 was divided from the product

$\:\:$

$\underline{\bold{\texttt{So the resultant will be :}}}$

$\:\:$

➠ [(6x) ÷ 76.2]

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Then,11.2 was added to the quotient

$\:\:$

$\underline{\bold{\texttt{So the resultant will be :}}}$

$\:\:$

➠ [(6x) ÷ 76.2] + 11.2

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Given that the final number is 12.2

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$\underline{\bold{\texttt{So the equation will be :}}}$

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➜ [(6x) ÷ 76.2] + 11.2 = 12.2

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➜ [(6x) ÷ 76.2] = 12.2 - 11.2

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➜ [(6x) ÷ 76.2] = 1

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So,

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➜ $\sf \dfrac { 6x } { 76.2 } = 1$

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⟮ Multiplying the above equation by 76.2 ⟯

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➜ $\sf \dfrac { 6x } { 76.2 } \times 76.2 = 1 \times 76.2$

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➜ $\sf \dfrac { 6x } { 1 } = 76.2$

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➜ 6x = 76.2

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➜ $\sf x = \dfrac { 76.2 } { 6 }$

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➨ x = 12.7

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• Hence the initial number was 12.7