Lucy baked 299 puffs and doughnuts. She burnt 13 pieces and counted the remaining pieces. ¹₆ of the doughnuts and ³₄ of the puffs were cheese flavoured. There were equal number of doughnuts and puffs that were cherry flavoured.

1. How many unburnt cherry puffs were there?
2. What fraction of the unburnt pastries were cheese puffs?

(a)
Number of pastries that was not burnt
= 299 - 13
= 286

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

Fraction of the puffs that was cherry flavoured
= 1 - ³₄ 
= ¹₄ 

The number of cherry doughnuts and cherry puffs was the same. Make the numerators the same. 
56 Doughnuts = 1x54x5 Puffs 
56 Doughnuts = 520 Puffs 

Number of unburnt doughnuts = 6 u
Number of unburnt puffs = 20 u

Total number of unburnt pastries
= 6 u + 20 u
= 26 u

26 u = 286

1 u = 286 ÷ 26 = 11

Number of unburnt cherry puffs
= 5 u
= 5 x 11
= 55

(b)
Number of unburnt cheese puffs
= 20 u - 5 u
= 15 u

^{Unburnt cheese puffs}_{Total unburnt pastries}
= ¹⁵_{6 + 20}
= ¹⁵₂₆

Answer(s): (a) 55; (b) ¹⁵₂₆