Gem baked 57 macarons and doughnuts. She burnt 19 pieces and counted the remaining pieces. ¹₄ of the doughnuts and ⁴₅ of the macarons were cranberry flavoured. There were equal number of doughnuts and macarons that were apple flavoured.

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

(a)
Number of pastries that was not burnt
= 57 - 19
= 38

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

Fraction of the macarons that was apple flavoured
= 1 - ⁴₅ 
= ¹₅ 

The number of apple doughnuts and apple macarons was the same. Make the numerators the same. 
34 Doughnuts = 1x35x3 Macarons 
34 Doughnuts = 315 Macarons 

Number of unburnt doughnuts = 4 u
Number of unburnt macarons = 15 u

Total number of unburnt pastries
= 4 u + 15 u
= 19 u

19 u = 38

1 u = 38 ÷ 19 = 2

Number of unburnt apple macarons
= 3 u
= 3 x 2
= 6

(b)
Number of unburnt cranberry macarons
= 15 u - 3 u
= 12 u

^{Unburnt cranberry macarons}_{Total unburnt pastries}
= ¹²_{4 + 15}
= ¹²₁₉

Answer(s): (a) 6; (b) ¹²₁₉