Question

The sum of two consecutive multiples of 5 is 65. Find the number.

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Answer 1

Correct Question-:

• The sum of two consecutive multiples of 5 is 65. Find the number.

AnswEr-:

• $\underline{\boxed{\star{\sf{\blue{ The\:two\:numbers \;are\:30\:and\:35. }}}}}$

EXPLANATION-:

• $\frak{Given \:\: -:} \begin{cases} \sf{The\:sum\:of\:two\:consecutive\:multiples\;of\:5\:is\:65.}\end{cases}$
• $\frak{To \:Find\: -:} \begin{cases} \sf{The\:\:number. .}\end{cases}$

Now ,

• $\frak{Let's \:Assume \: -:} \begin{cases} \sf{The\:first \:consecutive \:number \:be\:= \frak{5(x +1)}} & \\\\ \sf{Then,}& \\\\ \sf{The\:second \:consecutive \:number \:is\:= \frak{5(x +2)}}\end{cases}$

• Then ,
• $\frak{According \:To\:Question \: -:} \begin{cases} \sf{ The\:sum\:of\:two\:consecutive\:multiples\;of\:5\:is\:65.}& \\\\ \sf{Then,}& \\\\ \sf{Equation\:Formed =5(x+1)+5(x+2)=65}\end{cases}$

• Solving for x in Equation-: 5(x +1) + 5(x+2) = 65
• $\implies{\sf{\large { 5(x +1) + 5(x +2) =65 }}}$
• $\implies{\sf{\large { 5x +5 + 5x +10 =65 }}}$
• $\implies{\sf{\large { 5x +5x + 5 +10 =65 }}}$
• $\implies{\sf{\large { 10x + 15 =65 }}}$
• $\implies{\sf{\large { 10x =65-15 }}}$
• $\implies{\sf{\large { 10x =50 }}}$
• $\implies{\sf{\large { x =\frac{50}{10} }}}$
• $\implies{\sf{\large { x =5 }}}$

Therefore,

• $\underline{\boxed{\star{\sf{\blue{ x = 5 }}}}}$

Now ,

• $\frak{Putting \:x =5 \: -:} \begin{cases} \sf{The\:first \:consecutive \:number \:be\:= \frak{5(x +1)=5(5+1)=25+5=30}} & \\\\ \sf{Then,}& \\\\ \sf{The\:second \:consecutive \:number \:is\:= \frak{5(x +2)=5(5+2)=25+10=35}}\end{cases}$

Hence ,

• $\underline{\boxed{\star{\sf{\blue{ The\:two\:numbers \;are\:30\:and\:35. }}}}}$

______________________________

• Equation = 5(x +1) + 5(x+2) = 65
• Here,
• $\implies{\sf{\large { x =5 }}}$

Now ,

• Substitute the value x =5 in Equation.
• Equation = 5(x +1) + 5(x+2) = 65

• $\implies{\sf{\large { 5(5 +1) + 5(5 +2) =65 }}}$
• $\implies{\sf{\large { 25+5 + 25+10 =65 }}}$
• $\implies{\sf{\large { 30+35 =65 }}}$
• $\implies{\sf{\large { 65=65 }}}$

Therefore,

• $\underline{\boxed{\star{\sf{\blue{ LHS = RHS }}}}}$

• $\implies{\sf{\large { Hence\:,Verified. }}}$

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