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 By: 2000123 (offline)  Wednesday, June 06 2012 @ 07:17 PM CDT (Read 1043 times)
2000123

Q11.In a survey, some pupils were asked if they preferred volleyball or table-tennis.
13/20 of the pupils chose volleyball, 75% of the pupils chose table-tennis and 5% of the pupils
did not choose any of the two sports.Given that 90 pupils chose both volleyball and table-tennis,
how many pupils took part in the survey

Q14.Amy savings was 40% less than Baoyu's savings at first.After Amy donated
\$52 and Baoyu donated \$60, Baoyu savings became 5 times as much as Amy's.
What was their total savings at first

Junior

Registered: 03/07/12
Posts: 21

 By: awyw1201 (offline)  Wednesday, June 06 2012 @ 09:39 PM CDT
awyw1201

Quote by: 2000123

Q11.In a survey, some pupils were asked if they preferred volleyball or table-tennis.
13/20 of the pupils chose volleyball, 75% of the pupils chose table-tennis and 5% of the pupils
did not choose any of the two sports.Given that 90 pupils chose both volleyball and table-tennis,
how many pupils took part in the survey

Q14.Amy savings was 40% less than Baoyu's savings at first.After Amy donated
\$52 and Baoyu donated \$60, Baoyu savings became 5 times as much as Amy's.
What was their total savings at first

1)13/20 = 65%

% of pupils who chose both--> 65% + 75% - 95% = 45%

45%--> 90
1%-->2
100%--> 200

Ans: 200 pupils

2) Use units and parts

<at first>

A:B--> 3u:5u

<after>

A:B--> 1p:5p

3u - 52 = 1p---(1)
5u - 60 = 5p---(2)

(1) x 5, we have

15u - 260 = 5p

Thus,

5u - 60 = 15u -260
10u =200
1u =20
Total savings at first-->20 x 8 = 160

Ans: \$160

Regular Member

Registered: 07/08/11
Posts: 87

 By: echeewh (offline)  Wednesday, June 06 2012 @ 09:43 PM CDT
echeewh

Hey there,

Following pls find the worked solutions.

Q11.

V: 13/20
T: 75% = 3/4 = 15/20
None: 5% = 1/20

Total: 29/20

The extra 9/20 (or 9u) represents the number of pupils in the survey who preferred both V and T. In other words, this 9u is counted twice in the Total.

Given that 90 pupils chose both V and T, we have ...

9u --> 90
1u --> 10

Number of pupils who took part in survey:
= 20u --> 20 x 10
= 200

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

Q14

<before>
A : B
60 : 100
3 : 5

<process>
A donated \$52; B donated \$60

<After>
1 : 5

There are few methods / techniques to do this viz. model, cross-multiply or simultaneous / compare & replace (using parts n units). The latter method is provided by awyw1201. Hence the other 2 methods are provided here.

Concept used here is known as <Changed Qtys> and following is:

Method 1: Cross-Multiply

Based on the <before> and <After> ratio model above, using a top-down approach for A and B respectively, we have ...

(3u - 52) / 1 = (5u - 60) / 5

Apply Cross-Multiply technique, we have ...

5 x (3u - 52) = 1 x (5u - 60)
15u - 260 = 5u - 60

Rearranging 'like' terms as in Algebra, we have ...

15u - 5u --> 260 - 60
10u --> 200
1u --> 20

Total savings (at first) = 8u --> 8 x 20 = \$160

Method 2: Model

<before>

A |-------|-------|-------| (3u)
B |-------|-------|-------|-------|-------| (5u)

<process>
A donated \$52; B donated \$60

<After>
Since B donated \$60 and thereafter, remaining proportion becomes 5p, we can make use of B's original 5u (Before) and its 1u becomes (1u - 12).

Hence, B's final 1p = (1u - 12).

Given these data, we can now draw the respective models for A and B as shown:

A |----|--| (1u - 12)
***<-1p->

******-12
B |----|--|----|--|----|--|----|--|----|--| (5u - 60)
***<---------------5p----------------->

where |--| --> -12

Comparing <before> and <after> models for A, and since A donated \$52, we have ...

3u - (1u - 12) --> 52
2u + 12 --> 52
2u --> 52 - 12 = 40
1u --> 20

Total savings (at first) = 8u --> 8 x 20 = \$160

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

Trust the above helps.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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