Answer:
[tex]\qquad\qquad\qquad\boxed{ \sf{ \: \sf \: Number \:is \: 15 \: }} \\ \\ [/tex]
Step-by-step explanation:
Let assume that the number be x.
According to statement, if 10 be added to four times a certain number ,the result is 5 less than five times the number.
So,
[tex]\sf \: 4x + 10 = 5x - 5 \\ \\ [/tex]
[tex]\sf \: 4x - 5x = - 5 - 10 \\ \\ [/tex]
[tex]\sf \: - x = - 15 \\ \\ [/tex]
[tex]\sf\implies \sf \: x = 15 \\ \\ [/tex]
Hence,
[tex]\sf\implies \sf \: Number \:is \: 15 \\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional Information
[tex]\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \bigstar \: \bf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \bigstar \: \bf{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}[/tex]
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[tex] \underline{ \underline{ \sf \: Question - }}[/tex]
If 10 be added to four times a certain number ,the result is 5 less than five times the number . find the number.
[tex] \underline{ \underline{ \sf \:Let's \: Assume - }}[/tex]
Required number be x.
[tex] \underline{ \underline{ \sf \: Solution- }}[/tex]
We have,
[tex] \sf \: 10 \: be \: added \: to \: four \: times \: a \: \\ \sf \: certain \: number \implies \bf{10 + 4x}[/tex]
and,
[tex] \sf \: the \: result \: is \: 5 \: less \: than \: 5 \: times \: \\ \sf \: the \: number \implies \bf{5x - 5}[/tex]
now,
[tex] \pmb{According \: to \: the \: Question - }[/tex]
[tex] \bf \: 10 + 4x = 5x - 5[/tex]
[tex] \bf \: \: 10 + 5 = 5x - 4x[/tex]
[tex] \bf \: 15 = x[/tex]
or,
[tex] \bf \: x = 15[/tex]
the number is 15.
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Answers & Comments
Answer:
[tex]\qquad\qquad\qquad\boxed{ \sf{ \: \sf \: Number \:is \: 15 \: }} \\ \\ [/tex]
Step-by-step explanation:
Let assume that the number be x.
According to statement, if 10 be added to four times a certain number ,the result is 5 less than five times the number.
So,
[tex]\sf \: 4x + 10 = 5x - 5 \\ \\ [/tex]
[tex]\sf \: 4x - 5x = - 5 - 10 \\ \\ [/tex]
[tex]\sf \: - x = - 15 \\ \\ [/tex]
[tex]\sf\implies \sf \: x = 15 \\ \\ [/tex]
Hence,
[tex]\sf\implies \sf \: Number \:is \: 15 \\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional Information
[tex]\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \bigstar \: \bf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \bigstar \: \bf{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}[/tex]
Verified answer
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[tex] \underline{ \underline{ \sf \: Question - }}[/tex]
If 10 be added to four times a certain number ,the result is 5 less than five times the number . find the number.
__________________________________________________
[tex] \underline{ \underline{ \sf \:Let's \: Assume - }}[/tex]
Required number be x.
__________________________________________________
[tex] \underline{ \underline{ \sf \: Solution- }}[/tex]
We have,
[tex] \sf \: 10 \: be \: added \: to \: four \: times \: a \: \\ \sf \: certain \: number \implies \bf{10 + 4x}[/tex]
and,
[tex] \sf \: the \: result \: is \: 5 \: less \: than \: 5 \: times \: \\ \sf \: the \: number \implies \bf{5x - 5}[/tex]
now,
[tex] \pmb{According \: to \: the \: Question - }[/tex]
[tex] \bf \: 10 + 4x = 5x - 5[/tex]
[tex] \bf \: \: 10 + 5 = 5x - 4x[/tex]
[tex] \bf \: 15 = x[/tex]
or,
[tex] \bf \: x = 15[/tex]
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Hence,
the number is 15.
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