A teacher gave the same test to three history classes: M, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?  Choose the correct choice from the following answers:
A) 74  B) 75  C) 76  D) 77  E) 78
Ans : B (75)   lets say class M indeed has 4 children, B has 6 children and C has 5 children.   now, if the average of class M is 65, hence total marks awarded in the class = 65*4= 
<gadget id="calculator">65*4</gadget>
<output>260</output>
260   Similarly,   class B= 80*6= 
<gadget id="calculator">80*6</gadget>
<output>480</output>
480   class C= 77*5= 
<gadget id="calculator">77*5</gadget>
<output>385</output>
385   total marks provided= M+B+C = 260+480+385= 
<gadget id="calculator">260+480+385</gadget>
<output>1_125</output>
1125   avg. marks= 1125 / 15 (total no. of students) = 75=75
<result>B</result>
A teacher gave the same test to three history classes: M, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?