Gem baked 215 cupcakes and puffs. She burnt 17 pieces and counted the remaining pieces. ¹₄ of the puffs and ⁵₆ of the cupcakes were apple flavoured. There were equal number of puffs and cupcakes that were cherry flavoured.

1. How many unburnt cherry cupcakes were there?
2. What fraction of the unburnt pastries were apple cupcakes?

(a)
Number of pastries that was not burnt
= 215 - 17
= 198

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

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

The number of cherry puffs and cherry cupcakes was the same. Make the numerators the same. 
34 Puffs = 1x36x3 Cupcakes 
34 Puffs = 318 Cupcakes 

Number of unburnt puffs = 4 u
Number of unburnt cupcakes = 18 u

Total number of unburnt pastries
= 4 u + 18 u
= 22 u

22 u = 198

1 u = 198 ÷ 22 = 9

Number of unburnt cherry cupcakes
= 3 u
= 3 x 9
= 27

(b)
Number of unburnt apple cupcakes
= 18 u - 3 u
= 15 u

^{Unburnt apple cupcakes}_{Total unburnt pastries}
= ¹⁵_{4 + 18}
= ¹⁵₂₂

Answer(s): (a) 27; (b) ¹⁵₂₂