Answer:

A man is 37 years old and his two sons are 8 years and 3 years old. After how many

years will he be twice as old as the sum of the ages of his sons?

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(In Explanation)

Step-by-step explanation:

❍ Let the number of years in which his age will be twice as old as the sum of his sons be x years respectively.

Present age of Man is 37 years old and Present age of his first son is 8 years old and second one is 3 years old.

Therefore,

— In x years their ages;

Age of Man = (37 + x)

Age of First son = (8 + x)

Age of YOUNGER son = (3 + x)

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⠀⠀\qquad\quad{\underline{ \underline{ \pink{\bigstar\:\frak{ACCORDING \: to \: the \: Given \: Question :}}}}}

★AccordingtotheGivenQuestion:

⠀⠀

The age of FATHER will be twice as old as the sum of ages of his sons.

⠀⠀

Therefore,

⠀

★ Father's age = 2(Sum of ages of son) ★

⠀⠀

\begin{gathered}:\implies\sf (37 + x) = 2\Big[(8 + x) + (3 + x)\Big]\\\\\\:\implies\sf 37 + x = 2 (11 + 2x) \\\\\\:\implies\sf 37 + x = 22 + 4x\\\\\\:\implies\sf 3x = 15\\\\\\:\implies\sf x = \cancel\dfrac{15}{3}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 5}}}}}\;\bigstar\end{gathered}

:⟹(37+x)=2[(8+x)+(3+x)]

:⟹37+x=2(11+2x)

:⟹37+x=22+4x

:⟹3x=15

:⟹x=

3

15

:⟹

x=5

★

⠀⠀

\therefore{\underline{\textsf{After\;\textbf{5 years}\;his\;age\;will\;be\;twice\;as\;old\;sum\;of\;ages\;his\;sons.}}}∴

After5 yearshisagewillbetwiceasoldsumofageshissons.