Final answer:
To form words using all the letters of the word 'equation' such that the vowels and consonants occur together, we consider the vowels and consonants as two separate blocks. The number of words that can be formed is (2!) * (5!) * (3!), which is equal to 1440.
Step-by-step explanation:
To solve this problem, we need to first determine the number of vowels and consonants in the word 'equation'. 'Equation' has 5 vowels (e, u, a, i, o) and 3 consonants (q, t, n). To arrange the vowels and consonants together, we consider them as one block. So, we have 2 blocks - one with the 5 vowels and one with the 3 consonants. We can arrange these 2 blocks in (2!) ways. Within each block, the vowels or consonants can be arranged in their respective order in (5!) and (3!) ways respectively. Therefore, the total number of words that can be formed is (2!) * (5!) * (3!), which simplifies to 1440 words.