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(a) If Mrs Lim baked 5u chocolate cupcakes, she baked ( 288 – 5u ) vanilla cupcakes.

She sold 3u chocolate cupcakes and left with 2u, and she was left with ( 1 – 5/9) ( 288 – 5u ) = 

4( 288 -5u )/9 vanilla cupcakes.

2u + 4( 288 -5u )/9  = 122               multiply both sides by 9

18u + 1152 – 20u = 1098

2u = 54

u = 27

5(288 – 5u) /9 = 5 (288 – 135)/9=    765/9 = 85

She sold 85 vanilla cupcakes.

(b) She was left with 2u = 54 chocolate cupcakes and 288 – 5u – 85 = 68 vanilla cupcakes.

68 -54 = 14

So 14 fewer chocolate cupcakes than vanilla cupcakes were left. 

Check : 288 – 135 = 153      

2/5*135 = 54                 

4/9*153 = 68

68 + 54 = 122                  checked.

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