Kathy baked 112 doughnuts and puffs. She burnt 8 pieces and counted the remaining pieces. ¹₄ of the puffs and ²₃ of the doughnuts were cranberry flavoured. There were equal number of puffs and doughnuts that were apple flavoured.

1. How many unburnt apple doughnuts were there?
2. What fraction of the unburnt pastries were cranberry doughnuts?

(a)
Number of pastries that was not burnt
= 112 - 8
= 104

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

Fraction of the doughnuts that was apple flavoured
= 1 - ²₃ 
= ¹₃ 

The number of apple puffs and apple doughnuts was the same. Make the numerators the same. 
34 Puffs = 1x33x3 Doughnuts 
34 Puffs = 39 Doughnuts 

Number of unburnt puffs = 4 u
Number of unburnt doughnuts = 9 u

Total number of unburnt pastries
= 4 u + 9 u
= 13 u

13 u = 104

1 u = 104 ÷ 13 = 8

Number of unburnt apple doughnuts
= 3 u
= 3 x 8
= 24

(b)
Number of unburnt cranberry doughnuts
= 9 u - 3 u
= 6 u

^{Unburnt cranberry doughnuts}_{Total unburnt pastries}
= ⁶_{4 + 9}
= ⁶₁₃

Answer(s): (a) 24; (b) ⁶₁₃