1. **State the problem:** A consumer buys orange juice cartons of 3 liters and 1.5 liters. They buy a total of 33 liters and pay exactly 29.00. 2. **Define variables:** Let $x$ be the number of 3-liter cartons. Let $y$ be the number of 1.5-liter cartons. 3. **Write the linear equations:** Total liters equation: $$3x + 1.5y = 33$$ Total cost equation: $$2.5x + 1.5y = 29$$ 4. **Solve the system:** From the first equation: $$3x + 1.5y = 33$$ Divide both sides by 1.5: $$\cancel{3}x/\cancel{1.5} + \cancel{1.5}y/\cancel{1.5} = 33/1.5$$ $$2x + y = 22$$ From the second equation: $$2.5x + 1.5y = 29$$ Divide both sides by 0.5: $$\cancel{2.5}x/\cancel{0.5} + \cancel{1.5}y/\cancel{0.5} = 29/0.5$$ $$5x + 3y = 58$$ Use the first simplified equation to express $y$: $$y = 22 - 2x$$ Substitute into the second: $$5x + 3(22 - 2x) = 58$$ $$5x + 66 - 6x = 58$$ $$-x + 66 = 58$$ $$-x = 58 - 66$$ $$-x = -8$$ $$x = 8$$ Find $y$: $$y = 22 - 2(8) = 22 - 16 = 6$$ 5. **Answer:** The consumer buys 8 cartons of 3 liters and 6 cartons of 1.5 liters.