Final answer:
Juan weighs 30 kg and his father weighs 75 kg.
Step-by-step explanation:
To find the weights of Juan and his father, we can set up a system of equations using the given information. Let's assume the weight of Juan is 2x and the weight of his father is 5x, where x represents a common multiplier. We know that the sum of their weights is 105 kg, so we can write the equation 2x + 5x = 105. Combining like terms, we get 7x = 105. Dividing both sides by 7, we find that x = 15. Therefore, Juan weighs 2x = 2(15) = 30 kg, and his father weighs 5x = 5(15) = 75 kg.