Percentage P6 2009 SA2 P2 Catholic High Q15

Tom had $144 more than Ali at first. After Tom spent 25% of his money and Ali spent 1/3 of his money, Tom had $122 more than Ali. How much did Tom have at first? [5]


25/100 x 144 = $36
144 - 36 = $108

T [][][][][][][][][][][][][108][36]    25% = 1/4, Make 1/4 and 1/3 like fractions
A [][][][][][][][][][][][]                   1/4 = 3/12 and 1/3 = 4/12 

TN [][][][][][][][][][108]
AN [][][][][][][][]<122>

1 u --> 122 - 108 = 14

12 u --> 12 x 14 = 168

168 + 144 = $312

Tom had $312 at first.


Alternative method

T [   ][   ][   ] [   ]       [][22][][22][][22][][22]
A [][][]<  144  >        [][][]<-------144------->
            <122>22

TN [   ][   ][   ]       Comparing highlight
AN [][] <122>       [   ] --> [][22]


1 u --> 144 - 4 x 22 = 56

4 u --> 4 x 56 = 224

224 + 4 x 22 = $312

Tom had $312 at first.


Alternative method (Algebra)

4 T - 3 A --> $144

3 T - 2 A --> $122

1 T - 1 A --> 144 - 122 = 22

2 T - 2 A --> 2 x 22 = 44

1 T  --> 122 - 44 = 78

4 T --> 4 x 78 = $312

Tom had $312 at first.


Alternative method