In a certain room the ratio of males to females is 4 to 5. After 8 males enter the room, the ratio of males to females is 6 to 5. What is the total number of people in the room before the additional males enter the room?

Explanation

To solve this problem, start by defining variables for the number of males and females in the room. Let the number of males be 4x and the number of females be 5x, based on the initial ratio of 4 to 5.The equation for the initial setup is: 4x / 5x = 4 / 5 (which holds true by definition)When 8 additional males enter, the number of males becomes 4x + 8. The new ratio of males to females is given as 6 to 5:(4x + 8) / 5x = 6 / 5Cross-multiply to solve for x: 5(4x + 8) = 6(5x) 20x + 40 = 30x 10x = 40 x = 4Substitute x back to find the number of males and females: Number of males = 4x = 16 Number of females = 5x = 20The total number of people initially in the room is 16 + 20 = 36. Thus, the correct answer is (B) 36.Options A, C, and D result from incorrect calculations or assumptions in setting up the problem or solving the equations.