A costs rule is C(x) = 0.75x + 24000 and a sales rule is R(x) = 1.95x, both in dollars. How many units must be sold to break even?

1. Breaking even means the costs equal the money coming in, so set 0.75x + 24000 = 1.95x. 2. Take 0.75x from both sides to get 24000 = 1.2x. 3. Divide both sides by 1.2 to get x = 20000 units. 4. Check the costs: 0.75 dollars times 20,000 is 15,000 dollars, plus 24,000 dollars, which is 39,000 dollars. 5. Check the sales: 1.95 dollars times 20,000 is 39,000 dollars, so the two match. 6. Option D comes from dividing 24,000 by 0.75, which ignores the money coming in. 7. Option C simply repeats the fixed cost as though it were a count of units. 8. Option A comes from dividing 24,000 by 1.33, a rounded gap between the two rates. _Source: OpenStax College Algebra (CC BY 4.0), Ch 7 "Systems of Equations and Inequalities", section 7.1 Systems of Linear Equations: Two Variables_