5
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When Sam's father died, Sam's uncle, Matthew (his fathers only brother) was twice the age of Sam minus 14 years.

As Sam and Matthew grew older they became friends. When the younger of the two turned 35 the other was double his age minus 29 years.

Sam and Matthew were born in different years but share the same birthday.

How old was Matthew when his brother died?

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8
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$26$ Years

Because when younger one is $35$, other one is $(35\times 2)-29=41$. So $6$ years difference. So if Sam is age of $a$ when his father died, then Uncle is $2a-14$. Both's different is $4$ years. $(2a-14)-a=6 \Rightarrow a=20$, then Uncle must be $20+6=26$ years when his brother died.

Another possible can be $2$ Years

Because when younger one is $35$, other one is $(35\times 2)-29=41$. So $6$ years difference. So if Sam is age of $a$ when his father died, then Uncle is $2a-14$. Both have a difference of $4$ years. $a-(2a-14)=6 \Rightarrow a=8$, then Uncle must be $(2\times 8)-14= 2$ years when his brother died.

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  • $\begingroup$ Might want to check your calculations $\endgroup$ – Xylius Jun 9 '16 at 5:50
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    $\begingroup$ 2*35 is 70, 70-29 is 41, not 39 $\endgroup$ – Xylius Jun 9 '16 at 5:53
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    $\begingroup$ Nice try but as @xylius said you should double check your math. You can also check your work for with the formula for the age difference between Sam and Matthew at the time Matthew's brother (and Sam's dad) died. $\endgroup$ – studycrypto Jun 9 '16 at 5:55
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    $\begingroup$ Good work. You found one of two possible solutions. Is there another? $\endgroup$ – studycrypto Jun 9 '16 at 5:59
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    $\begingroup$ Well done! Uncle can be 2 and nephew 8 or Uncle can be 26 with nephew 20 $\endgroup$ – studycrypto Jun 9 '16 at 6:14
4
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When Younger one turned 35,

Older one turned $(35\times 2)-29=41$.Thus difference between their ages$=6$ years.

Thus,

Assuming Matt's age when his brother died$=x$ and Sam's age$=y$. We get 2 equations. $x-y=6$. And $2y-x=14$ (Which is given in the first line of the puzzle).

Hence, Solving, we get

Matthew's age$=26$ years and Sam's age$=20$ years.

EDIT: Apparently, there are two possible solutions.

If Matthew is younger than Sam, We, get Sam's age=8 years And Matthew's age= 2 years.

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  • $\begingroup$ Good work. You found one of two possible solutions. Is there another? $\endgroup$ – studycrypto Jun 9 '16 at 5:59
  • $\begingroup$ Don't tell me that Sam's uncle is younger than Sam. That contradicts the logic part of the puzzle. $\endgroup$ – Sid Jun 9 '16 at 6:00
  • $\begingroup$ The current age gap is absurd enough tbh, but then again, I do actually have an uncle younger than me $\endgroup$ – Xylius Jun 9 '16 at 6:01
  • $\begingroup$ @sid Your answer is correct, but because of the wording of the question the older party is unknown so there are two possible solutions $\endgroup$ – studycrypto Jun 9 '16 at 6:01
  • $\begingroup$ @sid Matthew could not have been 20 (with Sam 26) at the time because 2(26) -14 = 38 and you correctly discovered they must be 6 years apart not 18 years apart. $\endgroup$ – studycrypto Jun 9 '16 at 6:11
1
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When Sam's father died,

  • Sam was $x$ years old.
  • Matthew was $2x-14$ years old.

When Sam turned $35$ years old, Matthew became $(35\times2)-29=41$ years.a So the age gap between them is 6.

According to this,

$2x-14-x=6 \\ x-14=6 \\ x=6+14 \\ \therefore {x=20} $

Therefore, Matthew must have been $2x-14$

$$2x-14\\=2(20)-14\\=40-14\\=26$$

years old when his brorther died.

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-1
$\begingroup$

When Matthew's brother died,

  • Sam's age was $x$.
  • Matthew's age was $2x-14$.

When Sam turned 35,

Matthew became $(2\times35)-29=41$ years old. The age gap between them is $41-35=6$ years.

By the question,

At the time of his brother's death, Matthew's age was $2x-14$, while Sam was $x$ years old. The difference between the ages is $6$. So, our equation will be: $(2x-14)-x=6\\(2x-x)-14=6\\x-14=6\\x=14+6 \\ x=20$

Now that we know $x$,

Mathew must have been $x+6\\=20+6\\=26$ years old when his brother died.

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  • $\begingroup$ Other than formatting, how is this answer different from others already given, or specifically, from the answer originally given by @Akshat Agarwal? $\endgroup$ – Rubio Jun 25 '17 at 21:49
  • $\begingroup$ @Rubio Actually, what happened is I edited Akshat Agarwals's answer to its current form. When I later added this answer, it became identical to the other answer. I shouldn't have made so many changes to that answer... $\endgroup$ – Soha Farhin Pine Jun 26 '17 at 10:50

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