Shannon baked 121 cupcakes and doughnuts. She burnt 7 pieces and counted the remaining pieces. ¹₃ of the doughnuts and ⁷₈ of the cupcakes were chocolate chip flavoured. There were equal number of doughnuts and cupcakes that were blueberry flavoured.

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

(a)
Number of pastries that was not burnt
= 121 - 7
= 114

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

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

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

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

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

19 u = 114

1 u = 114 ÷ 19 = 6

Number of unburnt blueberry cupcakes
= 2 u
= 2 x 6
= 12

(b)
Number of unburnt chocolate chip cupcakes
= 16 u - 2 u
= 14 u

^{Unburnt chocolate chip cupcakes}_{Total unburnt pastries}
= ¹⁴_{3 + 16}
= ¹⁴₁₉

Answer(s): (a) 12; (b) ¹⁴₁₉