Shiyun baked 269 doughnuts and puffs. She burnt 8 pieces and counted the remaining pieces. ¹₅ of the puffs and ⁵₆ of the doughnuts were strawberry flavoured. There were equal number of puffs and doughnuts that were vanilla flavoured.

1. How many unburnt vanilla doughnuts were there?
2. What fraction of the unburnt pastries were strawberry doughnuts?

(a)
Number of pastries that was not burnt
= 269 - 8
= 261

Fraction of the puffs that was vanilla flavoured
= 1 - ¹₅ 
= ⁴₅ 

Fraction of the doughnuts that was vanilla flavoured
= 1 - ⁵₆ 
= ¹₆ 

The number of vanilla puffs and vanilla doughnuts was the same. Make the numerators the same. 
45 Puffs = 1x46x4 Doughnuts 
45 Puffs = 424 Doughnuts 

Number of unburnt puffs = 5 u
Number of unburnt doughnuts = 24 u

Total number of unburnt pastries
= 5 u + 24 u
= 29 u

29 u = 261

1 u = 261 ÷ 29 = 9

Number of unburnt vanilla doughnuts
= 4 u
= 4 x 9
= 36

(b)
Number of unburnt strawberry doughnuts
= 24 u - 4 u
= 20 u

^{Unburnt strawberry doughnuts}_{Total unburnt pastries}
= ²⁰_{5 + 24}
= ²⁰₂₉

Answer(s): (a) 36; (b) ²⁰₂₉