Jean baked 332 doughnuts and tarts. She burnt 8 pieces and counted the remaining pieces. ¹₆ of the tarts and ⁵₆ of the doughnuts were vanilla flavoured. There were equal number of tarts and doughnuts that were banana flavoured.

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

(a)
Number of pastries that was not burnt
= 332 - 8
= 324

Fraction of the tarts that was banana flavoured
= 1 - ¹₆ 
= ⁵₆ 

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

The number of banana tarts and banana doughnuts was the same. Make the numerators the same. 
56 Tarts = 1x56x5 Doughnuts 
56 Tarts = 530 Doughnuts 

Number of unburnt tarts = 6 u
Number of unburnt doughnuts = 30 u

Total number of unburnt pastries
= 6 u + 30 u
= 36 u

36 u = 324

1 u = 324 ÷ 36 = 9

Number of unburnt banana doughnuts
= 5 u
= 5 x 9
= 45

(b)
Number of unburnt vanilla doughnuts
= 30 u - 5 u
= 25 u

^{Unburnt vanilla doughnuts}_{Total unburnt pastries}
= ²⁵_{6 + 30}
= ²⁵₃₆

Answer(s): (a) 45; (b) ²⁵₃₆