Gwen baked 229 muffins and cupcakes. She burnt 20 pieces and counted the remaining pieces. ¹₄ of the cupcakes and ⁴₅ of the muffins were cherry flavoured. There were equal number of cupcakes and muffins that were vanilla flavoured.

1. How many unburnt vanilla muffins were there?
2. What fraction of the unburnt pastries were cherry muffins?

(a)
Number of pastries that was not burnt
= 229 - 20
= 209

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

Fraction of the muffins that was vanilla flavoured
= 1 - ⁴₅ 
= ¹₅ 

The number of vanilla cupcakes and vanilla muffins was the same. Make the numerators the same. 
34 Cupcakes = 1x35x3 Muffins 
34 Cupcakes = 315 Muffins 

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

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

19 u = 209

1 u = 209 ÷ 19 = 11

Number of unburnt vanilla muffins
= 3 u
= 3 x 11
= 33

(b)
Number of unburnt cherry muffins
= 15 u - 3 u
= 12 u

^{Unburnt cherry muffins}_{Total unburnt pastries}
= ¹²_{4 + 15}
= ¹²₁₉

Answer(s): (a) 33; (b) ¹²₁₉