Nora baked 165 doughnuts and macarons. She burnt 11 pieces and counted the remaining pieces. ¹₄ of the macarons and ⁵₆ of the doughnuts were cranberry flavoured. There were equal number of macarons and doughnuts that were chocolate chip flavoured.

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

(a)
Number of pastries that was not burnt
= 165 - 11
= 154

Fraction of the macarons that was chocolate chip flavoured
= 1 - ¹₄ 
= ³₄ 

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

The number of chocolate chip macarons and chocolate chip doughnuts was the same. Make the numerators the same. 
34 Macarons = 1x36x3 Doughnuts 
34 Macarons = 318 Doughnuts 

Number of unburnt macarons = 4 u
Number of unburnt doughnuts = 18 u

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

22 u = 154

1 u = 154 ÷ 22 = 7

Number of unburnt chocolate chip doughnuts
= 3 u
= 3 x 7
= 21

(b)
Number of unburnt cranberry doughnuts
= 18 u - 3 u
= 15 u

^{Unburnt cranberry doughnuts}_{Total unburnt pastries}
= ¹⁵_{4 + 18}
= ¹⁵₂₂

Answer(s): (a) 21; (b) ¹⁵₂₂