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 By: geniuskids (offline)  Friday, March 01 2013 @ 07:27 PM CST (Read 1527 times)
geniuskids

Q15. There were 3/5 as many boys as girls in a hall during recess. After recess, 18 boys and 16 girls entered the hall. Then there were 5/6 as many boys as girls.
(a) How many boys were there in the hall at first? Ans-12 boys
(b) What fraction of the total number of pupils in the hall after recess were girls. Give your answer in the simplest form. Ans-6/11

Q17. Ali has five times as many paper clips as Paul and 10 more. Natalie has one tenth of what Ali has and 4 more.
The number of paper clips that Natalie has is 3 fewer than Paul's.
(a) What is the total number of paper clips the three children have altogether?Ans-119
(b) How many of Ali's paper clips must be given to Paul if both of them want the same number of paper clips?Ans-37

Many thanks

Active Member

Registered: 11/12/11
Posts: 169

 By: leawshirlyn (offline)  Sunday, March 03 2013 @ 07:46 PM CST
leawshirlyn

Hi,

Q17)

A --> 5P + 10
N --> 1/10 (5P + 10) + 4
and N --> P-3

therefore,
1/10 (5P + 10) + 4 = P - 3
1/2 P = 8
P = 16
A = 5P + 10 = 90
N = P - 3 = 13
total = 119

hope it helps

Newbie

Registered: 05/05/12
Posts: 5

 By: leawshirlyn (offline)  Sunday, March 03 2013 @ 07:52 PM CST
leawshirlyn

Q17 b)

No. of clips to give to Paul --> (90 -16) /2 = 37

Newbie

Registered: 05/05/12
Posts: 5

 By: echeewh (offline)  Sunday, March 03 2013 @ 09:35 PM CST
echeewh

Hi there,

Following pls find my worked solutions:

Q15

<Before>
B : G
3 : 5

<process>
B: +18, G: +16

<after>
B : G
5 : 6

Applying <Changed Qtys> concept (both number of B and G increases), we can use <Cross Multiply> method as follows:

(3u + 18) / 5 = (5u + 16) / 6
6 × (3u + 18) = 5 × (5u + 16)
18u + 108 = 25u + 80
25u - 18u --> 108 - 80
7u --> 28
1u --> 4

(a)
B (at first) = 3u --> 3 × 4 = 12

(b)
G (after) = 5u + 16 --> (5 × 4) + 16
********* = 20 + 16 = 36

B (after) = 12 + 18 = 30

Total (B + G) (after) = 30 + 36 = 66

Fraction of G in hall after recess = 36 / 66 = 6 / 11

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

Q17

Model below is not drawn to scale (refer to the units beside for more precision)

A = 5p + 10
P = 1p
N = [(1/10) of (5p + 10)] + 4
To split the 5p into (1/10), the lowest common multiple is 10. So 1 part(p) of A is divided into 2 equal units(u). Hence,

A = 10u + 10,
P = 2u
N = [(1/10) of (10u + 10)] + 4 = (1u + 1) + 4 = 1u + 5

A: |--|--|--|--|--|--|--|--|--|--|<10>| --> 10u + 10
P: |--|--| --> 2u
N: |--|<5>| --> 1u + 5

P - N = 3
2u - (1u + 5) = 3
2u - 1u - 5 = 3
1u --> 8

(a)
Total paper clips (A + P + N) = (10u + 10) + 2u + (1u + 5)
= 13u + 15 --> (13 × 8) + 15
= 104 + 15 = 119

(b)
A = 10u + 10 --> (10 × 8) + 10 = 80 + 10 = 90
P = 2u --> 2 × 8 = 16
A - P = 90 - 16 = 74
74 ÷ 2 = 37

Number of paper clips given by A = 37

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

Trust this helps.

Do let me know again if there's further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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