Ratio
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A piggy bank contained a certain number of $1 coins, $0.50 coins and $0.20 coins in the ratio of 4:6:9. Dan took out Six $1 coins and exchanged them for $0.20 and $0.50 coins. When he put these coins back into the piggy bank, the ratio became 6:14:23
a) How many coins were there before the exchange
b) Find the amount of money in the piggy bank.
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it's a psle qn :(
they only method i can think of is guess and check
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work with the knowledge that 2 is even number, 5 is odd.
meaning, you can only change 5 $0.20 for 1 $1, and 2 $0.50 for 1 $1... no other combinations...
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final ratio
6:14:23 = 3:7:11.5
since 6 coins are moved,
1 unit = 6 coins
doing the double check now.
total value of coins changed = $6
hence, 0.2(2.5)(6)+0.5(6)=$6 (proven correct)
a) number of coins,
(4+6+9)(6)=.......
i think you get the point.
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U o level student u donno how to do psle maths?
ok la i also donno
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4 : 6 : 9 = 8 : 12 : 18
Compare 8 : 12 : 18 with 6 : 14 : 23
8 - 2 = 6
12 + 2 = 14
18 + 5 = 23
(i'm using model method here) meaning 1 box = 3 coins
sorry if it sounds very blur from here...
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ahha my method sounds like SexyChin's one
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Originally posted by kenn3th:
A piggy bank contained a certain number of $1 coins, $0.50 coins and $0.20 coins in the ratio of 4:6:9. Dan took out Six $1 coins and exchanged them for $0.20 and $0.50 coins. When he put these coins back into the piggy bank, the ratio became 6:14:23
a) How many coins were there before the exchange
b) Find the amount of money in the piggy bank.
ok, it is solved. :)you can either use the LCM or LCF method I think, i.e. lowest common multiple and multiply by 23 or something.
Here, I provide another method........
$1 = 2x$0.50 = 5X$0.20
Hence the 1 dollar ratio is 1:2:5 for 1 dollar changing.
First ratio must be equal to second ratio in terms of absolute money since the total amount of money remains unchanged.
Hence, 4:6:9 <== this ratio we incorporate into the 1 dollar changing ratio to convert to absolute money.
==> $4:$3:$1.8 = $8.80 (we assume ratio of 4 parts in 1 dollar is $4)
Next, 6:14:23 ==> converting to absolute money is $6:$7:$4.6 = $17.60
Knowing that both ratios must give back same amount of money, so $17.60 = 2x $8.80.
So, we divide the 2nd ratio by 2 ==> 3:3.5:2.3, which is the correct money, i.e. $3:$3.50:$2.30
Now, we can apply the lowest common factor or multiple rule, since for 20cent denomination we cannot ave $2.30.
The question states 6 $1 dollar is used up, so the difference of the 2 ratios for the 1st number has to be 6.
Multiplying both ratios by 6,
1st ratio: 24:18:10.8
2nd ratio: 18:21:13.8
So, answer is already out!
24-18=6 dollars less
21-18=3 dollars more of 50cents = 6 50 cents more
13.8-10.8=3 dollars more of 20cents = 15 20cents more.
and if you add 24+18+10.8 = 18+21+13.8 = $52.80 is the total amount of money in the piggy bank.
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Hi,
PSLE mathematics (especially the model method) is not easy and my trainee teachers struggle with it :P
Cheers,
Wen Shih -
Answer
$1 : 50¢ : 20¢
4 : 6 : 9 = 24 : 36 : 54
6 : 14 : 23 = 18 : 42 : 69 [[24 - 18 = 6]
24 + 36 + 54 = 114
a) There were 114 coins before the exchange.
24 x 1 + 36 x 0.50 + 54 x 0.20 = $52.80
b) There was $52.80 in the piggy bank.