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 By: drstevewu (offline)  Friday, October 19 2012 @ 08:23 AM CDT (Read 1800 times)
drstevewu

Hi, like to know how to solve the following Math questions:

1. A group of pupils scored an average of 92 marks in a Math test. The boys scored 90 on average while the girls scored 95 on average. What is the ratio of the number of boys to the numbers of girls in the group?

2. At a funfair, Tom collected 2960 points for playing games. Each easy level game earned 32 points and each difficult level games earned 25% as much points as each easy level game. If Tom played 20 times of more difficult games than easy level games, how many times did he play the difficult level games?

Thank you.

Junior

Registered: 04/20/10
Posts: 31

 By: echeewh (offline)  Sunday, October 21 2012 @ 09:08 PM CDT
echeewh

Hi there,

Still working on Q2 and btw, do u already have the answer to this?

Heres my worked solution for Q1.

Q1

Total marks (B ) = 90B
Total marks (G) = 95G
Average Total = (90B + 95G) / (B + G)

Given average total = 92, we have ...

(90B + 95G) / (B + G) = 92
(90B + 95G) = 92 × (B + G)
90B + 95G = 92B + 92G
92B - 90B = 95G - 92G
2B = 3G
(B/G) = (3/2)

Hence, B : G = 3 : 2

====================

Trust this helps.

Do let me know again if this is different from your Answerkey or if there's further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 By: drstevewu (offline)  Wednesday, October 24 2012 @ 10:24 AM CDT
drstevewu

Thanks Edward. Yes i have got an answer from a friend for question 2. The solution is as follows:

Each easy level game earns 32 points.

Each difficult level game wiil earn ----- 25% of 32 = 8 points.

Since Tom played 20 times of more difficult level games than easy level games;

20 x 8 = 160 (the extra points for the difficult level games)

2960 - 160 = 2800 (easy + difficult level games poins)

1 set of easy + difficult games points -------- 32 +8 = 40 points

2800 / 40 = 70 sets

Easy level games is 70 times

Difficult level games : 70 + 20 = 90

Tom played 90 times of difficult leve games.

Junior

Registered: 04/20/10
Posts: 31

 By: echeewh (offline)  Monday, October 29 2012 @ 02:41 AM CDT
echeewh

hey drstevewu,

In the course of resolving your Q2, I have come across some doubts and ambiguity in the statements. Anyway, this is just my personal opinion.

Referring to your friend's solution, it is showing T played 20 more difficult games than easy. And NOT "played 20 times of more difficult games than easy level games" as stated in question, per se. This is as follows:

------------------------

Easy level games is 70 times
Difficult level games : 70 + 20 = 90
Tom played 90 times of difficult level games.

------------------------

So if T had played 70 times easy games, then he would have played ( 21 x 70 = 1470 ) of difficult games, since D : E = 21 : 1.

Hence, based on your friend's solution, the statement should be "played 20 more difficult games than easy level games"

If this is the way the question is intended for, then obviously I have no problem doing it then.

Hence, in my opinion, the question is rather ambiguous. Phrasing in a question is very important as it helps the student to answer the question correctly; otherwise, it will become misleading.

==============

Kind regards,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 By: drstevewu (offline)  Tuesday, October 30 2012 @ 07:56 PM CDT
drstevewu

Hi Edward,

Noted your comments. I might have typed the "times" by error. Sorry for the confusing you all. Thank you so much for your kind reply..

Junior

Registered: 04/20/10
Posts: 31

 By: limys (online)  Wednesday, October 31 2012 @ 12:07 AM CDT
limys

hi drstevewu,

Based on ans of 70 times easy and 90 times difficult, the total points wld be :-
70*32 + 90*40 = 5840

and not 2960.

Assuming "20 more difficult games" and NOT "20 times more difficult games", check if following makes sense :-

20 more difficult games are 20*40=800

2960-800 = 2160

Easy + Diff = 32 + 40 =72

2160/72=30

Therefore 30 easy and (30+20) diff

cheers

Newbie

Registered: 10/03/09
Posts: 1

 By: echeewh (offline)  Wednesday, October 31 2012 @ 06:49 AM CDT
echeewh

hello limys,

The original solution is cool ..

You pointed out the following:

70*32 + 90* 40 = 5840

However, each Difficult game earned 8 points and not 40 as you pointed out above (see following extract from solution):

Each difficult level game wiil earn ----- 25% of 32 = 8 points.

Thus, (70 × 32) + (90 × 8) = 2240 + 720 = 2960

============

Best regards,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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