A science class has two times as many boys as girls. During the final examination of the year, the girls average 90 points each, and the class as a whole averages 80 points per person. What is the average score of the boys in the class?
Accepted Solution
A:
Answer:Average score of boys is 75.Step-by-step explanation:Let the number of boys in the class be = xLet the number of girls in the class be = ySince it is given that boys are twice in number than of girls thus we have2y = x ......................(i)By definition of average we have[tex]Average_{boys}=\frac{\sum Marks_{boys}}{x}[/tex]Similarly[tex]Average_{girls}=\frac{\sum Marks_{girls}}{y}[/tex][tex]Average_{class}=\frac{\sum Marks_{boys}+\sum Marks_{girls}}{x+y}.......(iii)[/tex]Now it is given that average score of class is 80 points per person Using this in the equation '3' we get[tex]80=\frac{\sum Marks_{girls}+\sum Marks_{boys}}{x+y}\\\\Average_{class}=\frac{\sum Marks_{girls}}{x+y} +\frac{\sum Marks_{boys}}{x+y}\\\\80=\frac{90y}{3y}+\frac{\sum Marks_{boys}}{x+\frac{x}{2}}\\\\80=30+\frac{\sum Marks_{boys}}{\frac{3x}{2}}\\\\50=\frac{2}{3}\times \frac{\sum Marks_{boys}}{x}\\\\\therefore Average_{boys}=\frac{3}{2}\times 50=75[/tex]