A positive number is 5 time another number. If 21 is added to both the numbers, then one of the new numbers become twice of other

2 thoughts on “A positive number is 5 time another number. If 21 is added to both the numbers, then one of the new numbers become twice of other”

1. [tex]\bf Given \:\:: \begin{cases}\sf A\: positive\: number\: is\: 5 \:time \:another\: number\:.\\\\ \qquad \bf AND \:, \:\\\\ \sf 21 \:is \:added \:to\: both\: the\: numbers,\: then\: one\: of \:the \:new\: numbers\:\\ \qquad \sf become\: twice \:of \:other\: new \:numbers\: .\end{cases}\\[/tex]

   Exigency To Find : The Original number .

   ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

   ⠀⠀❍ Let’s Assume the other number be a .

   ⠀⠀Therefore,

   ⠀⠀⠀⠀ For positive umber , Given that ;

   ⠀⠀⠀⠀⠀⠀▪︎⠀⠀A positive number is 5 times another number.

   [tex]\qquad :\implies \sf Positive \:number \:\: \: 5 \times Other\;number \: \\[/tex]

   [tex]\qquad :\implies \sf Positive \:number \:\:= \: 5 \times a \: \\[/tex]

   [tex]\qquad :\implies \sf Positive \:number \:\:= \: 5a \: \\[/tex]

   [tex]\qquad \therefore \:\:\underline{\pmb{\pink{\: Positive \:number \:\:= \: 5a }} }\:\:\bigstar \\[/tex]

   ⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\:According \:\: to \:\: Question \: \: \::}}\\[/tex]

   ⠀━━ If 21 is added to both the numbers, then one of the new numbers become twice of other new numbers.

   [tex]\qquad:\implies \sf 21 + Positive \:number \: = \: 2 \ ( \ Other\:number \:+ \:21 \ ) \\[/tex]

   [tex]\qquad:\implies \sf 21 + 5a \: = \: 2 \ ( \ a \:+ \:21 \ ) \\[/tex]

   [tex]\qquad:\implies \sf 21 + 5a \: = \: 2 a \:+ \:42 \ \\[/tex]

   [tex]\qquad:\implies \sf 5a \: = \: 2 a \:+ \:42 \ – 21 \: \\[/tex]

   [tex]\qquad:\implies \sf 5a \: = \: 2 a \:+ \: 21 \: \\[/tex]

   [tex]\qquad:\implies \sf 5a – \:2a \: = \: \: 21 \: \\[/tex]

   [tex]\qquad:\implies \sf 3a \: = \: \: 21 \: \\[/tex]

   [tex]\qquad:\implies \sf a \: = \: \: \dfrac{21}{3} \: \\[/tex]

   [tex]\qquad:\implies \sf a \: = \: \:\cancel {\dfrac{21}{3} }\: \\[/tex]

   [tex]\qquad:\implies \sf a \: = \: \: 7 \: \\[/tex]

   [tex]\qquad \therefore\:\: \underline{\pmb{\pink{\: a \: = \: \: 7 \: }} }\:\:\bigstar \\[/tex]

   ⠀⠀⠀⠀⠀⠀▪︎⠀⠀Here , a denotes Other number which is 7 .

   ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀AND ,

   ⠀⠀⠀⠀⠀⠀▪︎⠀⠀The Positive number is 5a = 5 × 7 = 35 .

   ⠀⠀⠀⠀⠀[tex]\therefore {\underline{ \sf \:Hence, \:The \: \:numbers\:are\:\bf 7 \:\:\sf and \: \bf 35 \:\sf, \:respectively\: .}}\\[/tex]

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2. ❍ Let’s say, that the other number be x.

   Given that,

   • A positive number is five times the other Number.

   ➟ Postive no. = 5 × (Other no.)

   ➟ Positive number = 5x

   ⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━

   [tex]\underline{\bigstar\:\boldsymbol{By \; given \: Condition\;:}}[/tex]⠀⠀

   • And it is given that, If 21 is added to both the numbers, then one of the new number become twice of other new numbers.

   ⠀

   ✰ Adding 21 to both numbers —

   • Other no. = (x + 21)
   • Postive no. = (5x + 21)

   ⠀⠀⠀

   Therefore,

   ⠀⠀⠀

   [tex]:\implies\sf 5x + 21 = 2(x + 21)\\\\\\:\implies\sf 5x + 21 = 2x + 42\\\\\\:\implies\sf 5x – 2x = 42 – 21\\\\\\:\implies\sf 3x = 21\\\\\\:\implies\sf x = \cancel\dfrac{21}{3}\\\\\\:\implies\underline{\boxed{\frak{\purple{x = 7}}}}\;\bigstar[/tex]

   ⠀⠀⠀

   Hence,

   • Other number, x = 7
   • Postive number, 5x = 5(7) = 35

   ⠀⠀

   [tex]\therefore{\underline{\textsf{Hence, the original numbers are \textbf{7}\:\sf{and}\;\textbf{35}\: \sf{respectively.}}}}[/tex]⠀⠀⠀⠀⠀⠀

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