Rachel baked 224 cupcakes and scones. She burnt 15 pieces and counted the remaining pieces. ¹₄ of the scones and ⁴₅ of the cupcakes were apricot flavoured. There were equal number of scones and cupcakes that were apple flavoured.

1. How many unburnt apple cupcakes were there?
2. What fraction of the unburnt pastries were apricot cupcakes?

(a)
Number of pastries that was not burnt
= 224 - 15
= 209

Fraction of the scones that was apple flavoured
= 1 - ¹₄ 
= ³₄ 

Fraction of the cupcakes that was apple flavoured
= 1 - ⁴₅ 
= ¹₅ 

The number of apple scones and apple cupcakes was the same. Make the numerators the same. 
34 Scones = 1x35x3 Cupcakes 
34 Scones = 315 Cupcakes 

Number of unburnt scones = 4 u
Number of unburnt cupcakes = 15 u

Total number of unburnt pastries
= 4 u + 15 u
= 19 u

19 u = 209

1 u = 209 ÷ 19 = 11

Number of unburnt apple cupcakes
= 3 u
= 3 x 11
= 33

(b)
Number of unburnt apricot cupcakes
= 15 u - 3 u
= 12 u

^{Unburnt apricot cupcakes}_{Total unburnt pastries}
= ¹²_{4 + 15}
= ¹²₁₉

Answer(s): (a) 33; (b) ¹²₁₉