
By: geniuskids (offline) Sunday, October 14 2012 @ 09:35 AM CDT (Read 3085 times)



geniuskids 
Hi, can someone pls help solved these questions!
Q6 : A pen costs $1.10 less than a file. Karin can either buy 48 files or 92 pens with all her money.
How much does a pen cost?
Q10 : Sue had $80 more than her brother. After Sue spent 25% of her money and her brother spent 75% of his money, they still had $420 left altogether.
(a) How much did Sue left in the end?
(b) Express the amount of money her brother had left as a fraction of the amount of money Sue had in the end. (Give your answer in the simplest form)
Q12 : Kindly refer to the test paper as there are diagrams.
Q16 : The mass of sand in Sack B was 1/4 the mass of sand in Sack A. After 52.5kg of the sand in Sack A and 10kg 150g of sand in Sack B was used, the mass of sand in Sack A was 1/2 the mass of sand in Sack B. What was the total mass in Sack A and Sack B at first?
Q17 :The ratio of the number of $2 notes and $5 notes Jamie had was 15:13. She exchanged 60 pieces of $2 notes for $5 notes.
She then had an equal number of $2 and $5 notes.
What was the total value of $2 and $5 notes Jamie had?
Q18: The average number of situps performed by 15 girls and some boys was 50.
The average number of situps performed by the girls was 80% of the average number of situps performed by all the pupils.
The average number of situps performed by the boys was 30% more than the average number of situps performed by the girls.
(a) What was the average number of sit ups performed by the girls?
(b) What percentage of teh pupils were boys?
Help needed Urgently!
Many thanks!

Active Member
Registered: 11/12/11 Posts: 169





By: echeewh (offline) Monday, October 15 2012 @ 01:18 AM CDT



echeewh 
Hey there,
Im afraid there just too many questions to do at one time. Appreciate that next time you split your 6 questions into 2 or 3 postings in order that others can / may also help respond to them.
Anyway, following are the worked solutions for 3 of these. (Q6, 10,16, 17, 18). Will complete the remaining question shortly after.
=======================
Q6
F  P = 110
F = 110 + P
48F = 48 × (110 + P) = 5280 + 48P
5280 + 48P = 92P
92P  48P = 5280
44P = 5280
P = 5280 ÷ 44 = 120
Hence cost of 1P = $1.20
=================
Q10
<Before>
S <80>
B 
<process>
S: 25% (1/4)
B: 75% (3/4)
Split the equal portions of S, B into 4 identical units (u).
<After>
S: 3u (of equal portion) + [(3/4) × 80] = 3u + 60
B: 1u
(a)
Hence
3u + 60 + 1u > 420
4u > 420  60 = 360
1u > 90
S (left): 3u + 60 > (3 × 90) + 60 = 270 + 60 = $330
(b)
B (left): 1u > $90
Fraction = 90 / 330 = 3/11
==========================
Q16
A : B
4 : 1
52.5 10.15
1 : 2
Apply <CrossMultiply> method, we have ...
(4u  52.5) / 1 = (1u  10.15) / 2
2 × (4u  52.5) = (1u  10.15)
8u  105 = 1u  10.15
8u  1u > 105  10.15
7u > 94.85
1u > 13.55
Total mass (A+B at first) = 5u > 5 × 13.55 = 67.75 kg
================================
Q17
<before>
$2 : $5
15 : 13
<Process>
60 pieces of $2 = $120
120 ÷ 5 = 24 (pieces of $5)
<before>
$2 : $5
15 : 13
60 +24
<after>
1 : 1
Apply <Cross Multiply> method, we have ...
(15u  60) / 1 = (13u + 24) / 1
15u  13u > 60 + 24
2u > 84
1u > 42
At first,
$2 Qty: 15u > 15 × 42 = 630
Value : 630 × 2 = $1260
$5 Qty: 13u > 13 × 42 = 546
Value : 546 × 5 = $2730
Hence, Total value = $1260 + $2730 = $3990
===========================
Q18
(a)
Avg situps (G) = (80/100) × 50 = 40
(b)
Avg situps (B ) = 1.3 x 40 = 52
Let number of boys = 1u
Avg situps (all pupils) = [(40 × 15) + (52 × 1u)] / (15 + 1u) = 50
(600 + 52u) = 50 × (15 + 1u)
600 + 52u = 750 + 50u
52u  50u > 750  600
2u > 150
1u > 75
% pupils (B ) = (75 / 90) × 100 = 83 1/3 %
=========================
Trust these help.
Do let me know if there's further clarification.
Cheers,
Edward

Active Member
Registered: 04/21/11 Posts: 623





By: echeewh (offline) Wednesday, October 17 2012 @ 07:27 PM CDT



echeewh 
Hey there,
18/10  Post worked solution for final Q12 ...
Q12.
(Fig1):
Vol of water + Vol of 8 blocks = 10 × 448
= 4480 cm3  (1)
Base Area = 448 = 8u (blocks) × B (where B = breadth of container)
B = 448 ÷ 8u > (56/u)
(Fig2):
Vol of water + Vol of 3 blocks = 22 x B x 3u
= 22 x (56/u) x 3u
= 3696 cm3  (2)
Vol of 5 blocks = 4480  3696 = 784
Vol of 8 blocks = (784 / 5) x 8 = 1254.4 cm3
in (1):
Vol of water = 4480  Vol of 8 blocks
= 4480  1254.4
= 3225.6 cm3
=================
Trust this helps.
Do let me know again if there's further clarification.
Cheers,
Edward

Active Member
Registered: 04/21/11 Posts: 623





By: geniuskids (offline) Friday, October 19 2012 @ 08:04 AM CDT



geniuskids 
Quote by: echeewhHey there,
Im afraid there just too many questions to do at one time. Appreciate that next time you split your 6 questions into 2 or 3 postings in order that others can / may also help respond to them.
Anyway, following are the worked solutions for 3 of these. (Q6, 10,16, 17, 18). Will complete the remaining question shortly after.
=======================
Q6
F  P = 110
F = 110 + P
48F = 48 × (110 + P) = 5280 + 48P
5280 + 48P = 92P
92P  48P = 5280
44P = 5280
P = 5280 ÷ 44 = 120
Hence cost of 1P = $1.20
=================
Q10
<Before>
S <80>
B 
<process>
S: 25% (1/4)
B: 75% (3/4)
Split the equal portions of S, B into 4 identical units (u).
<After>
S: 3u (of equal portion) + [(3/4) × 80] = 3u + 60
B: 1u
(a)
Hence
3u + 60 + 1u > 420
4u > 420  60 = 360
1u > 90
S (left): 3u + 60 > (3 × 90) + 60 = 270 + 60 = $330
(b)
B (left): 1u > $90
Fraction = 90 / 330 = 3/11
==========================
Q16
A : B
4 : 1
52.5 10.15
1 : 2
Apply <CrossMultiply> method, we have ...
(4u  52.5) / 1 = (1u  10.15) / 2
2 × (4u  52.5) = (1u  10.15)
8u  105 = 1u  10.15
8u  1u > 105  10.15
7u > 94.85
1u > 13.55
Total mass (A+B at first) = 5u > 5 × 13.55 = 67.75 kg
================================
Q17
<before>
$2 : $5
15 : 13
<Process>
60 pieces of $2 = $120
120 ÷ 5 = 24 (pieces of $5)
<before>
$2 : $5
15 : 13
60 +24
<after>
1 : 1
Apply <Cross Multiply> method, we have ...
(15u  60) / 1 = (13u + 24) / 1
15u  13u > 60 + 24
2u > 84
1u > 42
At first,
$2 Qty: 15u > 15 × 42 = 630
Value : 630 × 2 = $1260
$5 Qty: 13u > 13 × 42 = 546
Value : 546 × 5 = $2730
Hence, Total value = $1260 + $2730 = $3990
===========================
Q18
(a)
Avg situps (G) = (80/100) × 50 = 40
(b)
Avg situps (B ) = 1.3 x 40 = 52
Let number of boys = 1u
Avg situps (all pupils) = [(40 × 15) + (52 × 1u)] / (15 + 1u) = 50
(600 + 52u) = 50 × (15 + 1u)
600 + 52u = 750 + 50u
52u  50u > 750  600
2u > 150
1u > 75
% pupils (B ) = (75 / 90) × 100 = 83 1/3 %
Understand up to last portion: do not understand why 75/90 x100 (where do u get 90? Can explain pls.tks
Trust these help.
Do let me know if there's further clarification.
Cheers,
Edward

Active Member
Registered: 11/12/11 Posts: 169





By: echeewh (offline) Friday, October 19 2012 @ 07:47 PM CDT



echeewh 
Hi there,
Question is (b) What percentage of the pupils were boys?
Boys = 75; Girls =15 (given in question)
Total (B+G) = 75 + 15 = 90
Hence, Fraction (B/Total) = (75/90)
=================
Trust the explanation helps.
Cheers,
Edward

Active Member
Registered: 04/21/11 Posts: 623





By: geniuskids (offline) Friday, October 19 2012 @ 09:02 PM CDT



geniuskids 
Thanks Edward. I managed to figure out 90 last night.
Thanks alot

Active Member
Registered: 11/12/11 Posts: 169



