Fraction P6 A002

Takumi went for a holiday trip to Thailand with his wife. His wife spent 2/9 of the money on buying clothes while Takumi spent 2/5 of the money on sports shoes and shorts. 1/4 of the remaining amount was spent on food. 3/5 of the remaining money was spent on a spa package for both of them. His wife spent 1/2 of the remaining money plus $6 to buy a pair of watch. Takumi used the remaining amount to play games in a casino and won an amount equals to 1/7 of the amount of money left. After using 2/7 of the remaining amount to pay for the airport tax and taxi fare, he is left with $120.

a) How much did he bring for his trip?

b) What fraction of money did his wife spent on buying clothes and watch?

5/7 r1 -- > 120

r1 -- > 7/5 x 120 = 168

8/7 r2 -- > 168

r2 -- > 7/8 x 168 = 147

If possible do the first 2 steps in 1 go.

7/8 x 7/5 x 120 = 147

1/2 r3 -- > 147 + 6 = 153

r3 -- > 2 x 153 = 306

2/5 r4 --> 306

r4 -- > 5/2 x 306 = 765

3/4 r5 -- > 765

r5 -- > 4/3 x 765 = 1020

17/45 -- > 1020

1 -- > 45/17 x 1020 = $2700

If possible do the previous 3 steps in 1 go.

45/17 x 4/3 x 5/2 x 306 = $2700

a) He brought $2700 for his trip.

2/9 x 2700 = 600

153 + 6 = 159

600 + 159 = 759

759/2700 = 253/900

b) His wife spent 253/900 of the money on clothes and watch.

Alternative Method

The model is broken into two parts because of plus $6. We cannot managed fraction / ratio together with $ at the same time.

       <$120>

[ 2 ][   5     ]  x 8

[    7      ][1]  x 7

40 u -- > $120

49 u -- > 49/40 x 120 = $147

2/9 x 5/5 = 10/45

2/5 x 9/9 = 18/45

45 – 10 – 18 = 17

Note: The units are not drawn to scale as we only want to focus on equating those remainings.

[                              17             ][  18  ][10]   x 4 x 5

[                         3                ][1]                  x 17 x 5

[                2                  ][ 3 ]                       x 17 x 3

[          ][$6][        1        ]                             x 17 x 3

<$147>

17 x 3 = 51

45 x 4 x 5 = 900

51 u -- > 147 + 6 = $153

900 u -- > 900/51 x 153 = $2700

a) He brought $2700 for his trip.


10 x 4 x 5 = 200

200 + 51 = 251

251 u -- > 251/51 x 153 = $753

753 + 6 = $759

759/2700 = 253/900


b) His wife spent 253/900 of the money on clothes and watch.