Kimberly baked 122 cupcakes and wafers. She burnt 18 pieces and counted the remaining pieces. ¹₆ of the wafers and ³₄ of the cupcakes were cheese flavoured. There were equal number of wafers and cupcakes that were blueberry flavoured.

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

(a)
Number of pastries that was not burnt
= 122 - 18
= 104

Fraction of the wafers that was blueberry flavoured
= 1 - ¹₆ 
= ⁵₆ 

Fraction of the cupcakes that was blueberry flavoured
= 1 - ³₄ 
= ¹₄ 

The number of blueberry wafers and blueberry cupcakes was the same. Make the numerators the same. 
56 Wafers = 1x54x5 Cupcakes 
56 Wafers = 520 Cupcakes 

Number of unburnt wafers = 6 u
Number of unburnt cupcakes = 20 u

Total number of unburnt pastries
= 6 u + 20 u
= 26 u

26 u = 104

1 u = 104 ÷ 26 = 4

Number of unburnt blueberry cupcakes
= 5 u
= 5 x 4
= 20

(b)
Number of unburnt cheese cupcakes
= 20 u - 5 u
= 15 u

^{Unburnt cheese cupcakes}_{Total unburnt pastries}
= ¹⁵_{6 + 20}
= ¹⁵₂₆

Answer(s): (a) 20; (b) ¹⁵₂₆