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 By: suz (offline)  Thursday, May 12 2011 @ 06:38 PM CDT (Read 1735 times)
suz

Can anyone help me to solve the following sa1 paper from Ai Tong :
1. The ratio of the number of \$100 notes to \$5 notes that Angel had was 7:4. She exchanged 12 pieces of \$100 notes for some \$5 notes. After which, the ratio of the number of \$100 notes to \$5 notes became 1:16. What was the amount of money Angel had?

From ACS
2. Keane bought some marbles and gave half of them to Leone. Leone bought some stamps and gave half of them to Keane.
Kean used 5 stamps and Leone gave away 11 marbles. The ratio of the number of stamps to the number of marbles Keane had left then became 1:7 and ratio of the number of stamps to the number of marbles Leon had left became 1:5.
How may stamps did Leone buy?

Newbie

Registered: 12/31/06
Posts: 5

 By: Patsy Goh (offline)  Thursday, May 12 2011 @ 11:06 PM CDT
Patsy Goh

Hi suz

http://www.kiasuparents.com/kiasu/forum ... start=2440

Newbie

Registered: 04/02/10
Posts: 4

 By: suz (offline)  Saturday, May 14 2011 @ 01:35 AM CDT
suz

Thanks Patsy for the help. Have manage to solve number 2 question, number 1 still stump me. Am looking at the link now for solution 1. thnks again.

Newbie

Registered: 12/31/06
Posts: 5

 By: ycthun (offline)  Saturday, May 14 2011 @ 05:47 PM CDT
ycthun

Here's another solution:

\$100:\$5
7 : 4
Every \$100 gives 20 \$5

After transfer of 12 \$100 notes, ratio becomes 1 : 16

Hence every drop in unit \$100 adds 20 \$5
Working backwards, possible ratios would be:

6 : 24
5 : 44
4 : 64 -----> 1 : 16

Hence 3u = 12 & 1u = 4
\$100 ------> 7u ----->28 x 100 ---->\$2800
\$5 -----> 4u ----> 16 x 5 ------> \$80
total originally \$2800

Hope this helps

Ted

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Registered: 06/23/09
Posts: 8

 By: gladiator (offline)  Saturday, May 14 2011 @ 10:07 PM CDT

Another method is to compare the values of the notes.

Number
\$100:\$5
7 : 4

Convert to total value of respective notes (\$100 -> 20*\$5) becomes
140 : 4
Total no of units = 144

Now you change some \$100 notes into \$5 notes. But the total amount of money remained the same. So...

Converting the final ratio of the number of notes into the values
1:16 becomes 20:16

Total units = 36

144/36 = 4

This means that 1 unit in the ratio 20:16 is 4 times the value of 1 unit in the ratio 140:4.

140 : 4 -> 20*4 : 16*4 = 80 : 64

Since she exchanged 12 \$100 notes for \$5 notes,

60u = \$1200
144u = \$1200/60*144 = \$2880

PS Ted you made a small careless mistake at the end

Newbie

Registered: 03/19/11
Posts: 3

 By: ycthun (offline)  Sunday, May 15 2011 @ 01:12 AM CDT
ycthun

Oops. Total should be \$2880. Typo error

Newbie

Registered: 06/23/09
Posts: 8

 By: suz (offline)  Tuesday, May 17 2011 @ 09:33 PM CDT
suz

Thank you Ted and gladiator for the alternative solutions.

Newbie

Registered: 12/31/06
Posts: 5

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