Cindy baked 58 doughnuts and cupcakes. She burnt 13 pieces and counted the remaining pieces. ¹₃ of the cupcakes and ²₃ of the doughnuts were vanilla flavoured. There were equal number of cupcakes and doughnuts that were chocolate chip flavoured.

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

(a)
Number of pastries that was not burnt
= 58 - 13
= 45

Fraction of the cupcakes that was chocolate chip flavoured
= 1 - ¹₃ 
= ²₃ 

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

The number of chocolate chip cupcakes and chocolate chip doughnuts was the same. Make the numerators the same. 
23 Cupcakes = 1x23x2 Doughnuts 
23 Cupcakes = 26 Doughnuts 

Number of unburnt cupcakes = 3 u
Number of unburnt doughnuts = 6 u

Total number of unburnt pastries
= 3 u + 6 u
= 9 u

9 u = 45

1 u = 45 ÷ 9 = 5

Number of unburnt chocolate chip doughnuts
= 2 u
= 2 x 5
= 10

(b)
Number of unburnt vanilla doughnuts
= 6 u - 2 u
= 4 u

^{Unburnt vanilla doughnuts}_{Total unburnt pastries}
= ⁴_{3 + 6}
= ⁴₉

Answer(s): (a) 10; (b) ⁴₉