Can somebody please give me some advice on a mathematical problem involving averages?

A total of 60 sophomores and juniors were given a history test. The 45 juniors had an average score of 85 while the 15 sophomores had an average of 90. What was the average score for all 60 students who took the test?





This is in an ACT test prep booklet, but they do not provide the answer. I tried the problem on my own, though. I want to know if I'm right.





I ended up getting 86.2% as the final answer. I'm pretty sure this is right, but I'm not 100% comfortable with deriving the answer. Could anyone please explain it in simple terms?Can somebody please give me some advice on a mathematical problem involving averages?
Well, the average of each junior is 85 (judging by the explanation).


The average of each sophomore is 90.





So, it is:


((15*90)+(45*85))/60=x if x is the average of all 60 students





x=86.25%Can somebody please give me some advice on a mathematical problem involving averages?
(45*85)+(15*90)=5175


5175/60=86.25%


I think you are right.
An average is calculated by summing all the individual scores and then dividing by the number of students.








((45 x 85) + (15 x 90)) / 60 = 86.25


Looks like you're right!
Given that there are 15 sophomores and 45 juniors, we multiply the average for each group by the number of people in each group.





Juniors: 45x85=3825


Sophomores: 15x90=1350





Now, we add these up and divide by 60.





3825+1350=5175, 5175/60=86.25





Pretty close... the answer is 86.25%.





Good luck on the ACT!

makeup techniques