1. **State the problem:** We have three pencil cases A, B, and C with a total of 96 crayons. 2. **Given information:** - Pencil case A has $\frac{1}{6}$ of the total crayons. - Pencil case B has 12 fewer crayons than pencil case C. 3. **Define variables:** Let the number of crayons in pencil case C be $x$. 4. **Express other quantities in terms of $x$:** - Crayons in A: $\frac{1}{6} \times 96 = 16$ - Crayons in B: $x - 12$ 5. **Write the total crayons equation:** $$16 + (x - 12) + x = 96$$ 6. **Simplify and solve for $x$:** $$16 + x - 12 + x = 96$$ $$2x + 4 = 96$$ $$2x = 92$$ $$x = 46$$ 7. **Find crayons in B:** $$B = x - 12 = 46 - 12 = 34$$ 8. **Summarize results:** - Pencil case A: 16 crayons - Pencil case B: 34 crayons - Pencil case C: 46 crayons These add up to $16 + 34 + 46 = 96$ crayons, confirming the solution is correct.