Question

The sum of three consecutive even numbers is 126. What is the difference between twice the lowest one and one-half of the highest one?

Answer is 58 how ​

Answer 1

$\red{\circledast}\:$Let the consecutive even numbers be 2x, 2x + 2, 2x + 4.

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$\underline{\bigstar\:\boldsymbol{According \;to \;the\: given \;Question\; :}}$

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• ${\sf{\pink{2x\:+\:2x\:+\:2\:+\:2x\:+\:4\:=\:126}}}$

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Therefore,

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$\:\:\:\:\:\:\:\:\:\:\succ{\sf{6x\:+\:6\:=\:126}}$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\succ{\sf{6x\:=\:126\:-\:6}}$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\succ{\sf{6x\:=\:120}}$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\succ{\sf{x\:=\:{\dfrac{120}{6}}}}$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\succ{\sf{\bold{x\:=\:20}}}$

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Hence,

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• $\sf{Lowest\:term\:=\:2\:\times\:20\:\times\:120\:=\:{\bold{40}}}$
• $\sf{Highest\:term\:=\:2\:\times\:20\:+\:4\:=\:{\bold{44}}}$

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Required Difference,

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$\:\:\:\:\:\:\:\:\succcurlyeq\:\sf{2\:\times\:40\:-\:{\dfrac{1}{2}}\:\times\:44}$

$\:\:\:\:\:\:\:\:\succcurlyeq\:\sf{80\:-\:22\:=\:58}$

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Hence,

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$\:\:\:\:\:\:\:\:\:\therefore\:{\underline{\sf{So,\:the\:difference\:is\:{\textsf{\textbf{58 }}}}}}.$

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$\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━$

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