A canner has 2 products: citrus and tropical, the citrus has 70% orange juice and 30% mango juice, the tropical has 80% mango juice and 20% orange juice. How many liters of each product can I pack if I have 450 of orange and 800 liters of mango?

Let C be the number of liters of citrus product. Let T be the number of liters of tropical product. To solve this problem, you can set up a system of linear equations based on the given information and then solve for the number of liters of each product you can pack. Let's use variables to represent the number of liters of each product: Let C be the number of liters of citrus product. Let T be the number of liters of tropical product. Based on the question two equations: For orange juice: 0.70C + 0.20T = 450 -> 7C + 2T = 4500 For mango juice: 0.30C + 0.80T = 800 -> 3C + 8T = 4000 Solving two equations, (7C + 2T) - (3C + 8T) = 4500 - 4000 Simplify: 4C - 6T = 500 Now, isolate C: 4C = 500 + 6T Divide both sides by 4: C = 125 + 1.5T 0.70(125 + 1.5T) + 0.20T = 450 Now, solve for T: 87.5 + 1.05T + 0.20T = 450 Combine like terms: 1.25T = 450 - 87.5 1.25T = 362.5 Now, divide by 1.25 to find T: T = 362.5 / 1.25 T = 290 Now, Put the value of T to calculate C, C = 125 + 1.5T C = 125 + 1.5(290) C = 125 + 435 C = 560