Students averaged 84% on test; 20 boys averaged 82%; find 30 girls' average

[S52 Power]

Students in a particular math class received an average score of 84% on a recent test. If there are 20 boys and 30 girls in the class, and the boys’ average score was 82%, what was the girls’ average score?
Answer= 85%

what equation would I use to solve?

 

[Dr.Peterson]

Students in a particular math class received an average score of 84% on a recent test. If there are 20 boys and 30 girls in the class, and the boys’ average score was 82%, what was the girls’ average score?
Answer= 85%

what equation would I use to solve?

I'd use the definition of average, rather than look for some formula dedicated to this problem. You could write a single equation to represent it, but you don't have to.

If the average of 20 scores is 82, what is the total of those scores?

If the average of 50 scores is 84, what must the total of those scores be?

What is the total of the girls' scores? What is their average?

 

[Steven G]

Students in a particular math class received an average score of 84% on a recent test. If there are 20 boys and 30 girls in the class, and the boys’ average score was 82%, what was the girls’ average score?
Answer= 85%

what equation would I use to solve?

You need to add up all 50 scores, then divide by 50 and set it equal to 84.
Let g = avg score for the girls.
The boys avg of 82 means that it is like each boy scored 82.

So we have (82+82+82+82+82+82+82+82+82+82+82+82+82+82+82+82+82+82+82+82+g+g+g+g+g+g+g+g+g+g+g+g+g+g+g+g+g+g+g+g+g+g+g+g+g+g+g+g+g+g)/50 = 84

(20*82 + 30g)/50 = 84
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