Problem: an astronomer noted that a grouping of red giant stars had an average solar mass of 8 m each , and a grouping of white dwarf stars had an average solar mass of 1.5 m each . if the astronomer calculated the total solar mass of both groupings to be 49 m , what total number of red giant stars and white dwarf stars did the astronomer note ?
Rationale: we can determine quickly that total number should range between 49 / 8 < = n < = 49 / 1.5 , so ans should be between 6 and 33 . now solving the expression 8 a + 1.5 b = 49 decreasing 49 in multiple of 8 and checking divisibility of that number by 1.5 . this way we get 2 red giants , 22 white dwarfs we get 49 , but 2 + 22 = 24 and 24 is not an option . next we get 5 red giants and 6 white dwarfs to get 49 , 5 * 8 + 6 * 1.5 = 49 hence total number is 5 + 6 = 11 ans b
annotated_formula: add(divide(subtract(49, multiply(1.5, add(const_2, const_4))), 8), add(const_2, const_4))