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.......

Percentage P5 2009 SA2 Catholic High

18. Mrs Lim bought some bowls and plates.If she buys another 5 bowls, there are 60% as many bowls as plates. If she buys another 9 plates, there will be thrice as many plates as bowls. How many bowls did she buy?


B [         ][5]
   [   ][   ][   ]
P [   ][   ][   ][   ][   ]

B [         ]
    [   ][   ][   ][   ][   ][   ][   ][   ][    ] Compare
    [         ][          ][          ]< 5 x 3 >
P  [                          ][  9  ]  Compare

4 u --> 9 + 5 x 3 = 24  [9 u - 5 x 3 --> 5 u + 9]
1 u --> 24 ÷ 4 = 6

3 x 6 - 5 = 13 bowls

She bought 13 bowls.


Alternative method

  B      P
+ 5
------------
 60  : 100 = 3 : 5
------------

5 x (B + 5) --> 3 x P
5 B + 25 --> 3 P

 B      P
       + 9
----------
 1   :   3
----------

3 B --> P + 9

3 P --> 3 x (3 B - 9) = 9 B - 27

9 B - 27 --> 5 B + 25
4 B --> 25 + 27 = 52
B --> 52 ÷ 4 = 13 bowls

She bought 13 bowls.