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 By: Dahlia98 (offline)  Thursday, September 23 2010 @ 01:58 AM CDT (Read 1777 times)
Dahlia98

Appreciate advice on how to solve these questions?

Q 1
After a quiz, Jean and her friends calculated the average of their
scores. They noted that if Jean could get 20 marks more, they would
have an average of 80 marks. However, if she could get 4 marks more,
their average would become 78. How many friends did Jean have?

Q 2
The average score of a test by a class was 60 marks. After two pupils
who scored an average of 96 marks left the class, the average score of
the remaining pupils became 58 marks. How many pupils were there in
the class at first?

Q 3
In the recent Channel W singing competition of 80 singers, the average
score was 58.5 marks. Given that the average score of the female
singers was 64 and that of the male singers was 56, find the number of
male singers who participated in the competition.

Q4
A group of pupils calculated their average score for an online quiz.
They found out that if one of them scored another 18 points, their
average score would be 85. However, if one of them scored 9 point
lesser, their average score would be 82. How many pupils were there in
the group?

Newbie

Registered: 11/03/09
Posts: 2

 By: tanhuimin (offline)  Thursday, September 23 2010 @ 10:26 PM CDT
tanhuimin

Q 1
After a quiz, Jean and her friends calculated the average of their scores. They noted that if Jean could get 20 marks more, they would have an average of 80 marks. However, if she could get 4 marks more, their average would become 78. How many friends did Jean have?

Increase of 16 marks only add on 2 marks to the average scores,
The no. of children involve in the quiz --> 16 / 2 = 8
Ans : Jean’s has 7 friends.

Q 2
The average score of a test by a class was 60 marks. After two pupils who scored an average of 96 marks left the class, the average score of the remaining pupils became 58 marks. How many pupils were there in the class at first?

Base on the fact that the average score increases by 2marks after the add in of 96 marks x 2pax, we may draw the model,

From the model,
96 x 2 = 192
192 - 58 – 58 = 76
76 / 2 = 38
Ans : There were 38 pupils in the class at first.

Q 3
In the recent Channel W singing competition of 80 singers, the average score was 58.5 marks. Given that the average score of the female singers was 64 and that of the male singers was 56, find the number of male singers who participated in the competition.

Use Guess and Check.
80 singers, Average score 58.5 --> total score = 80 x 58.5 = 4680
Since the average score of female is much higher than the overall average score, that means the no. of female must be less than half of the total no. of singers, so we setup a Guess and Check table

No. of Females | No. of Males | Total Score | Tally 4680 ?
30 | 50 |30 x 64 + 50 x 56 = 4720 | No.
25 | 55 |25 x 64 + 55 x 56 = 4680 | Yes!
Please refer to attached jpg for the Guess and Check table.
Ans : No. of male singers is 55

Q4
A group of pupils calculated their average score for an online quiz. They found out that if one of them scored another 18 points, their average score would be 85. However, if one of them scored 9 point
lesser, their average score would be 82. How many pupils were there in the group?

similar to Question No. 1
+ 18 points --> Average 85
-9 point --> Average 82
18 + 9 = 27
To increase the average score by 3 points, that is from 82 to 85, it required an increase of 27 points in the total score.
No. of pupils = 27 / 3 = 9

Junior

Registered: 12/31/06
Posts: 18

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