In a high school class, the average score on a test among girls was 92.6, while the average score among boys was 83.0. The average score for the class was 89. If there are 16 students in the class, which of the following represents the relationship between the number of girls (g) and boys (b) in the class?
a) g+4=b
b) g+2=b
c) g=b
d) g - 2=b
e) g - 4=b
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phoenix9801
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The class average (89) is much closer to the girls' average (92.6) than to the boys' average (83), implying that the number of girls is much greater than the number of boys.phoenix9801 wrote:In a high school class, the average score on a test among girls was 92.6, while the average score among boys was 83.0. The average score for the class was 89. If there are 16 students in the class, which of the following represents the relationship between the number of girls (g) and boys (b) in the class?
a) g+4=b
b) g+2=b
c) g=b
d) g - 2=b
e) g - 4=b
Thus, the correct answer almost certainly is E, which implies that the number of girls is 4 more than the number of boys.
The sum of the scores for all 16 students = 16*89 = 1424.
Answer choice E, rephrased: g = b+4.
Since there are 16 students, and 4 more girls than boys, b=6 and g=10.
Sum of the scores for 6 boys with an average score of 83 and 10 girls with an average score of 92.6 = 6*83 + 10*92.6 = 498+926 = 1424.
Success!
The correct answer is E.
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LalaB
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92.6F+83M=89F+89N
F+M=16
=====
3F=5M
F+M=16
F=10
M=6
10-4=6
SO, E IS THE ANSW
F+M=16
=====
3F=5M
F+M=16
F=10
M=6
10-4=6
SO, E IS THE ANSW
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Since the overall class average (89) is closer to the girls' average (92.6) than it's to the boys' average (83), there must be more girls than boys. This narrows to choice D or E as the correct answer. If choice D is the correct answer, then we have:phoenix9801 wrote:In a high school class, the average score on a test among girls was 92.6, while the average score among boys was 83.0. The average score for the class was 89. If there are 16 students in the class, which of the following represents the relationship between the number of girls (g) and boys (b) in the class?
a) g+4=b
b) g+2=b
c) g=b
d) g - 2=b
e) g - 4=b
b + g = 16
g - 2 + g = 16
2g = 18
g = 9
So b = 16 - 9 = 7. Now let's check the overall class average by calculating the weighted average:
Average = (9 x 92.6 + 7 x 83)/16 = 1414.4/16 = 88.4
Answer choice D does not yield the given overall class average of 89. So the correct answer must be E.
Answer: E
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