Solve 1.35 = C - 0.15B for C, and then for B.

Step-by-step solution

1. 1

   Recognise it as a literal equation. There are two unknowns and one equation, so no single numeric answer exists. The task is to make one letter the subject: express it in terms of the other.

2. 2

   Solve for C. The term $-0.15B$ is subtracted from $C$, so undo it by adding $0.15B$ to both sides: $1.35 + 0.15B = C, \qquad \text{i.e. } C = 1.35 + 0.15B.$

3. 3

   Start the rearrangement for B by isolating its term. Subtract $C$ from both sides: $1.35 - C = -0.15B$. Keeping the minus sign attached to $0.15B$ at this stage prevents the classic sign flip.

4. 4

   Divide by the coefficient of B. Dividing by $-0.15$ gives $B = \frac{1.35-C}{-0.15} = \frac{C-1.35}{0.15}.$ Multiplying numerator and denominator by $100$ yields the cleaner $B = \dfrac{100C-135}{15} = \dfrac{20C-27}{3}$.

5. 5

   Cross-check the two forms against each other. Substituting $C = 1.35+0.15B$ into $\tfrac{C-1.35}{0.15}$ gives $\tfrac{0.15B}{0.15}=B$, so the two rearrangements are genuinely inverse to one another.

6. 6

   Test with a number. If $B = 4$ then $C = 1.35 + 0.6 = 1.95$; feeding that back, $B = \tfrac{1.95-1.35}{0.15} = \tfrac{0.6}{0.15} = 4$, as expected.