
By: geniuskids (offline) Friday, March 01 2013 @ 07:27 PM CST (Read 1390 times)



geniuskids 
Hi there, please help with these 2 questions:
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? Ans12 boys
(b) What fraction of the total number of pupils in the hall after recess were girls. Give your answer in the simplest form. Ans6/11
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?Ans119
(b) How many of Ali's paper clips must be given to Paul if both of them want the same number of paper clips?Ans37
Please help!
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 > P3
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: 625



