Percentage P5 2009 SA2 P2 Q17 Ai Tong

A seamstress had some white and some black buttons.60% of the buttons were white.He bought another 120 buttons.Now the percentage of white buttons became only 40% of the total.How many white buttons did he have at first?


W      B
---------
3   :   2 ---- 5 units
+ 120
---------
2   :   3 ----- 5 parts
---------

5 p --> 5 u + 120
1 p --> 1 u + 120/5 = 1 u + 24

2 p --> 2 u + 2 x 24 = 2 u + 48

3p --> 3u + 3 x 24 = 3 u + 72


3 u + ? --> 2 u + 48
2 u + (120 - ?) --> 3 u + 72

Both equations will end up with 1 u --> 48 -


Solution 1
-----------
W [][][][][][]
B  [][][][][][][][][]

5 u --> 120
1u --> 120 /5 = 24

W: 6 u --> 6 x 24 = 144 white buttons.


Solution 2
------------
W [][][][][][][][]
B  [][][][][][][][][][][][]

10 u --> 120
1u --> 120/10 = 12

W: 6 u --> 12 x  6 = 72 white buttons.


Solution 3
-----------
W [][][][][][][][][][][][][][]
B  [][][][][][][][][][][][][][][][][][][][][]

15 u --> 120
1 u --> 120/15 = 8

W: 12 u --> 12 x 8 = 96 white buttons.

etc.......