A jewelry maker incurs costs for a necklace according to $$ C(x)=39 x+1650 $$ If the revenue function for the necklaces is $$ R(x)=69 x $$ how many necklaces must be sold to break even? $$ \square $$

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The jewelry maker must sell 55 necklaces to break even. To find the break-even point, we need to set the cost function $$ C(x) $$ equal to the revenue function $$ R(x) $$. The break-even point occurs when total costs equal total revenue. Given the functions: $$ C(x) = 39x + 1650 $$ $$ R(x) = 69x $$ We set them equal to each other: $$ 39x + 1650 = 69x $$ Now, we can solve for $$ x $$: 1. Subtract $$ 39x $$ from both sides: $$ 1650 = 69x - 39x $$ $$ 1650 = 30x $$ 2. Divide both sides by 30: $$ x = \frac{1650}{30} $$ $$ x = 55 $$ Thus, the jewelry maker must sell $$ \boxed{55} $$ necklaces to break even.

A jewelry maker incurs costs for a necklace according to \[ C(x)=39 x+1650 \] If the revenue function for the necklaces is \[ R(x)=69 x \] how many necklaces must be sold to break even? \( \square \)

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A jewelry maker incurs costs for a necklace according to \[ C(x)=39 x+1650 \] If the revenue function for the necklaces is \[ R(x)=69 x \] how many necklaces must be sold to break even? \( \square \)

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