Emily baked 419 biscuits and cupcakes. She burnt 9 pieces and counted the remaining pieces. ¹₆ of the cupcakes and ⁶₇ of the biscuits were cheese flavoured. There were equal number of cupcakes and biscuits that were apple flavoured.

1. How many unburnt apple biscuits were there?
2. What fraction of the unburnt pastries were cheese biscuits?

(a)
Number of pastries that was not burnt
= 419 - 9
= 410

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

Fraction of the biscuits that was apple flavoured
= 1 - ⁶₇ 
= ¹₇ 

The number of apple cupcakes and apple biscuits was the same. Make the numerators the same. 
56 Cupcakes = 1x57x5 Biscuits 
56 Cupcakes = 535 Biscuits 

Number of unburnt cupcakes = 6 u
Number of unburnt biscuits = 35 u

Total number of unburnt pastries
= 6 u + 35 u
= 41 u

41 u = 410

1 u = 410 ÷ 41 = 10

Number of unburnt apple biscuits
= 5 u
= 5 x 10
= 50

(b)
Number of unburnt cheese biscuits
= 35 u - 5 u
= 30 u

^{Unburnt cheese biscuits}_{Total unburnt pastries}
= ³⁰_{6 + 35}
= ³⁰₄₁

Answer(s): (a) 50; (b) ³⁰₄₁