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The ratio of Sam's age to his son John's age is 8:3. If the sum of their ages is 55 years, what is the age difference between John and his dad in years?

So, I divided 55 by 11 and got 5, then multiplied that by 8 to get Sam's age (40), then the obvious remaining 15 years belong to John.

According to the answer key, the answer is 25. Can someone please explain how it is 25?

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    $\begingroup$ Who's Adam????? $\endgroup$ – barak manos Dec 31 '14 at 6:41
  • $\begingroup$ Sorry, it was an error. $\endgroup$ – John Dec 31 '14 at 6:44
  • $\begingroup$ @John And $40-15$ is... $\endgroup$ – Przemysław Scherwentke Dec 31 '14 at 6:50
  • $\begingroup$ you have got age of sam and john i.e $40$ and $15$.In question age difference is asked so difference is $40-15=25$. clear? $\endgroup$ – iostream007 Dec 31 '14 at 6:56
  • $\begingroup$ @Przemysław Scherwentke: On your homepage I think you want to say that English is not your mother tongue $\endgroup$ – miracle173 Dec 31 '14 at 7:51
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${s \over j} = { 8 \over 3}$ gives $3 s -8 j = 0$, and $s+j = 55$.

Solving gives $s=40, j=15$. The difference is 25.

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  • $\begingroup$ You're solving using substitution, right? $\endgroup$ – John Dec 31 '14 at 6:45
  • $\begingroup$ Yes. It is the simplest here. $\endgroup$ – copper.hat Dec 31 '14 at 6:48
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Given, $8:3$ multiply both sides by $x$, $8x:3x$, Now sum of their ages is $55$.

$8x+3x=55$

$11x=55$

$x=5$,

John's age, $=3\cdot x= 5\cdot3=15, $ and that of his father,$=8\cdot 5$=40

Difference, $=40-15=25$

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