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.
