1. **Problem Statement:** A consumer buys orange juice in 3-Liter cartons and 1.5-Liter cartons. They buy a total of 33 Liters and pay exactly 29.00. 2. **Define variables:** Let $x$ = number of 3-Liter cartons. Let $y$ = number of 1.5-Liter cartons. 3. **Write the equation for total liters:** Each 3-L carton has 3 Liters, each 1.5-L carton has 1.5 Liters. Total liters equation: $$3x + 1.5y = 33$$ 4. **Write the equation for total cost:** 3-L carton costs 2.50, 1.5-L carton costs 1.50. Total cost equation: $$2.5x + 1.5y = 29$$ 5. **Solve the system:** From the first equation: $$3x + 1.5y = 33$$ Divide both sides by 1.5: $$\cancel{\frac{3x}{1.5}} + \cancel{\frac{1.5y}{1.5}} = \frac{33}{1.5}$$ $$2x + y = 22$$ From the second equation: $$2.5x + 1.5y = 29$$ Multiply the simplified first equation by 1.5 to align $y$ terms: $$1.5(2x + y) = 1.5(22)$$ $$3x + 1.5y = 33$$ Subtract this from the second equation: $$2.5x + 1.5y - (3x + 1.5y) = 29 - 33$$ $$2.5x - 3x + 1.5y - 1.5y = -4$$ $$-0.5x = -4$$ Divide both sides by -0.5: $$\cancel{\frac{-0.5x}{-0.5}} = \frac{-4}{-0.5}$$ $$x = 8$$ 6. **Find $y$:** Use $2x + y = 22$: $$2(8) + y = 22$$ $$16 + y = 22$$ $$y = 22 - 16 = 6$$ **Final answer:** The consumer buys 8 cartons of 3 Liters and 6 cartons of 1.5 Liters.