Nicole baked 209 cupcakes and macarons. She burnt 6 pieces and counted the remaining pieces. ¹₅ of the macarons and ⁵₆ of the cupcakes were blueberry flavoured. There were equal number of macarons and cupcakes that were banana flavoured.

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

(a)
Number of pastries that was not burnt
= 209 - 6
= 203

Fraction of the macarons that was banana flavoured
= 1 - ¹₅ 
= ⁴₅ 

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

The number of banana macarons and banana cupcakes was the same. Make the numerators the same. 
45 Macarons = 1x46x4 Cupcakes 
45 Macarons = 424 Cupcakes 

Number of unburnt macarons = 5 u
Number of unburnt cupcakes = 24 u

Total number of unburnt pastries
= 5 u + 24 u
= 29 u

29 u = 203

1 u = 203 ÷ 29 = 7

Number of unburnt banana cupcakes
= 4 u
= 4 x 7
= 28

(b)
Number of unburnt blueberry cupcakes
= 24 u - 4 u
= 20 u

^{Unburnt blueberry cupcakes}_{Total unburnt pastries}
= ²⁰_{5 + 24}
= ²⁰₂₉

Answer(s): (a) 28; (b) ²⁰₂₉