# Ratios with Ages

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?

• Who's Adam????? – barak manos Dec 31 '14 at 6:41
• Sorry, it was an error. – John Dec 31 '14 at 6:44
• @John And $40-15$ is... – Przemysław Scherwentke Dec 31 '14 at 6:50
• 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? – iostream007 Dec 31 '14 at 6:56
• @Przemysław Scherwentke: On your homepage I think you want to say that English is not your mother tongue – miracle173 Dec 31 '14 at 7:51

${s \over j} = { 8 \over 3}$ gives $3 s -8 j = 0$, and $s+j = 55$.

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

• You're solving using substitution, right? – John Dec 31 '14 at 6:45
• Yes. It is the simplest here. – copper.hat Dec 31 '14 at 6:48

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, $=40-15=25$