Rachel baked 210 doughnuts and muffins. She burnt 20 pieces and counted the remaining pieces. ¹₃ of the muffins and ⁷₈ of the doughnuts were banana flavoured. There were equal number of muffins and doughnuts that were blueberry flavoured.

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

(a)
Number of pastries that was not burnt
= 210 - 20
= 190

Fraction of the muffins that was blueberry flavoured
= 1 - ¹₃ 
= ²₃ 

Fraction of the doughnuts that was blueberry flavoured
= 1 - ⁷₈ 
= ¹₈ 

The number of blueberry muffins and blueberry doughnuts was the same. Make the numerators the same. 
23 Muffins = 1x28x2 Doughnuts 
23 Muffins = 216 Doughnuts 

Number of unburnt muffins = 3 u
Number of unburnt doughnuts = 16 u

Total number of unburnt pastries
= 3 u + 16 u
= 19 u

19 u = 190

1 u = 190 ÷ 19 = 10

Number of unburnt blueberry doughnuts
= 2 u
= 2 x 10
= 20

(b)
Number of unburnt banana doughnuts
= 16 u - 2 u
= 14 u

^{Unburnt banana doughnuts}_{Total unburnt pastries}
= ¹⁴_{3 + 16}
= ¹⁴₁₉

Answer(s): (a) 20; (b) ¹⁴₁₉