Solve for k: 7200 = 200k + 300.

Step-by-step solution

1. 1

   Recognise the shape. This is a fixed-cost-plus-rate model: a base of $300$ plus $200$ per unit of $k$ totals $7200$. Such equations arise whenever a total splits into a setup charge and a per-item charge.

2. 2

   Remove the constant first. Subtract $300$ from both sides — the constant was added last, so it comes off first:

   $7200-300=200k\qquad\Longrightarrow\qquad 6900=200k$

3. 3

   Estimate before dividing. $200\times35=7000$, which slightly overshoots $6900$, so expect $k$ a little under $35$.

4. 4

   Divide by 200.

   $k=\frac{6900}{200}=\frac{69}{2}$

   Dividing numerator and denominator by $100$ gives the exact fraction $\tfrac{69}{2}$; since $69$ is odd, it does not reduce to an integer.

5. 5

   Convert to a decimal.

   $k=\frac{69}{2}=34.5$

   This terminates exactly (denominator $2$), unlike answers with denominators of $3$ or $7$ — and it matches the estimate of just under $35$ ✓.

6. 6

   Verify in the original equation. $200\times34.5+300=6900+300=7200$ ✓, exactly the left side. Note that if $k$ had to be a whole number of items, this problem would have no valid answer — worth checking against context.