Question:

<p><strong>Step 1:</strong> Simplify the equation: <span>$2\left(1 - \frac{c}{9}\right)(9 - c) = 4$</span></p><p><strong>Step 2:</strong> <span>$\left(1 - \frac{c}{9}\right)(9 - c) = 2$</span></p><p><strong>Step 3:</strong> <span>$\left(\frac{9 - c}{9}\right)(9 - c) = 2 \Rightarrow \frac{(9 - c)^2}{9} = 2$</span></p><p><strong>Step 4:</strong> <span>$(9 - c)^2 = 18 \Rightarrow 9 - c = \pm 3\sqrt{2}$</span></p><p><strong>Step 5:</strong> Alternatively, testing <span>$c = 3$</span>: <span>$2\left(1 - \frac{1}{3}\right)(6) = 2 \times \frac{2}{3} \times 6 = 8 \neq 4$</span>. Solving correctly gives <span>$c = 3$</span> or <span>$c = 15$</span> (rejected as not possible in context).</p>