Answer:
[tex]\large \boxed{46 }[/tex]
Explanation:
y = 4x² - 368x + 53
It would be easy to find the minimum using calculus, but we can also do it using algebra.
The standard form of the equation for a parabola is
y =ax² + bx + c
a = 4; b = -368; c = 53
The vertex is the point at which the parabola crosses its axis of symmetry. At that point,
[tex]x = -\dfrac{b}{2a} = -\dfrac{-368}{2\times4} = \dfrac{368}{8} = \mathbf{46}\\\\\text{Charles must repair at least $\large \boxed{\textbf{46 watches}}$ to have the lowest cost.}[/tex]
The graph below shows that Charles' cost is a minimum at 46 watches.
