Rudy measures a certain number of centimeters His older brother, José, beats him by 19 centimeters His little sister, measures just half of what José measures. But his uncle, the tallest in the family measures twice what José measures, plus twice what the little sister measures, minus twice what Rudy measures. Together they add up to 509 centimeters. How tall is each one? ANSWER

Let's represent the height of Rudy as R. According to the information given, José's height would be R + 19. The height of the little sister would be (R + 19)/2. And the height of the uncle would be 2(José) + 2(little sister) - 2(Rudy). Adding up all the heights, we get R + (R + 19) + (R + 19)/2 + 2(R + 19) + 2((R + 19)/2) - 2R = 509. Simplifying the equation, we have R + R + 19 + (R + 19)/2 + 2R + 38 + R + 19 - 2R = 509. Combining like terms, (11R + 113)/2 = 509. Multiplying both sides by 2, 11R + 113 = 1018. Subtracting 113 from both sides, 11R = 905. Dividing both sides by 11, R = 82.27. So, Rudy's height is approximately 82.27 centimeters. José's height is R + 19 = 82.27 + 19 = 101.27 centimeters. The little sister's height is (R + 19)/2 = (82.27 + 19)/2 = 50.64 centimeters. And the uncle's height is 2(José) + 2(little sister) - 2(Rudy) = 2(101.27) + 2(50.64) - 2(82.27) = 202.55 centimeters. Rudy = 82.27 centimeters José = 101.27 centimeters little sister = 50.64 centimeters uncle = 202.55 centimeters