Let j be the number of books that Jim has, c for Charles books, and b for Bob.
The word equation can be written as the following set of linear equations:
j = 3 x c
c = 2/3 x b
And they give you b = 27
So
c = 2/3 x 27
Doing this the very long way :)
= 2/3 x 27/1 ... make 27 an improper fraction (27/1)
= (2 x 27) / (3 x 1) ... multiplication of fractions means multiply numerators and denominators together
= (2 x (3 x 3 x 3)) / 3 ... factorizing 27 into 3 x 3 x 3
You can divide 3 from both numerator and denominator
2 x 3 x 3 = 18
So Charles has 18 books
And
j = 3 x c
= 3 x 18
= 54
So Jim has 54 books
Check your factorizations here:
http://statsfiddle.info/Primes/PrimeFactors/27