Ratios with Ages

Question

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?

Answer 1

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

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

Answer 2

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, $=40-15=25$