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Robin is twice as old as Earl, and in 6 years he will be three times as old as Adam, who is 8 years younger than Earl. Find their present ages.

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ANSWER

Earl =12 years, Robin =24 years and Adam =4 years.


EXPLANATION

Let Earl's present age be

[tex]e \: \: years[/tex]
Then Robin will be,


[tex]2e \: \: years[/tex]

and Adam will be

[tex](e - 8) \: \: years[/tex]


In six years time, Robin will be 3 times as old as Adam. This implies that,


[tex]2e + 6= 3(e - 8 + 6)[/tex]


[tex]2e + 6= 3(e - 2)[/tex]

We expand to get,


[tex]2e + 6= 3e - 6[/tex]



Group similar terms to get;

[tex]3e - 2e = 6 + 6[/tex]


This implies that,

[tex]e = 12[/tex]

Therefore their present ages are;

Earl =12 years, Robin =24 years and Adam =4 years.

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