Decimal P6 2010 SA2 Maha Bodhi P2 Q6

Mrs Gopal and Mrs Ari went to the supermarket. Both women decided to spend all their money on either apples or pears and they would not buy the same fruit.
If Mrs Gopal bought only pears, she would have 9 more fruit than Mrs Ari.
If she bought only apples, she would have 41 more fruit than Mrs Ari.
How much more money has Mrs Gopal than Mrs Ari?
 
 
40 : 60 = 2 : 3    Number bought   3 : 2 (inverse)
 
Number
G [          ][          ]
A [   ][   ][    ]<9>
 
2 u --> 3 p + 9
 
6 u --> 9 p + 3 x 9 = 9 p + 27
 
 
Number
G [          ][          ][          ]
A [   ][   ]<----- 41 ------>
 
3 u --> 2 p + 41
 
6 u --> 4 u + 2 x 41 = 4 p + 82
 
9 p + 27 --> 4 p + 82
 
5 p --> 82 - 27 = 55
 
1 p --> 55/5 = 11
 
3 p --> 3 x 11 = 33
 
2 u --> 33 + 9 = 42
 
 
42 x 0.60 = $25.20
 
33 x 0.40 = $13.20
 
25.2 - 13.20 = $12
 
It was $12


Alternatively
---------------

40 : 60 = 2 : 3   Number bought  3 : 2 (inverse)


Number


G [          ][          ]
A [   ][   ][   ]<9>




Number


G [          ][         ][          ]
A [   ][   ]<----- 41 ------>


5 u --> 5 p + 9 + 41 = 5 p + 50


5 u - 5 p --> 50


2 u - 2 p --> 2/5 x 50 = 20        Compare only number of pears bought


20 x 0.60 = $12


It was $12.