From: Jayden Sim
Date: October 6, 2011 13:55:19 GMT+08:00
To: chengliang chang <changchengliang@gmail.com>
Hi Mr Chang,Please help me with this question :A coin box contained some twenty-cent and fifty-cent coins in the ratio of 4 : 5. When 16 fifty-cent coins were taken out and replaced by some twenty-cent coins, the ratio then became 8 : 7. The total value of the twenty-cent coins added was the same as the total value of the fifty-cent coins taken out. Find the sum of money in the coin box.___
My Solution:
20cents 50cents
-------- ---------
4u : 5u
+ 40 -16 {40 x 20cent coins = 16 x 50cent coins}
--------------------
8 : 7
Try to balance the left and right branches.
To do that I purposely multiply the left branch by 7 and right branch by 8. (since the LCM of 8 and 7 is 56)
Now, if we are to balance the left and right branch:
28u + 280 = 40u - 128
408 = 12 u
1u = 408 / 12 = 34
Total amount:
4 x 34 x $0.20 + 5 x 34 x $0.50
= $27.20 + $85
= $112.20
