Olivia baked 466 muffins and puffs. She burnt 6 pieces and counted the remaining pieces. ¹₆ of the puffs and ⁷₈ of the muffins were vanilla flavoured. There were equal number of puffs and muffins that were banana flavoured.

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

(a)
Number of pastries that was not burnt
= 466 - 6
= 460

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

Fraction of the muffins that was banana flavoured
= 1 - ⁷₈ 
= ¹₈ 

The number of banana puffs and banana muffins was the same. Make the numerators the same. 
56 Puffs = 1x58x5 Muffins 
56 Puffs = 540 Muffins 

Number of unburnt puffs = 6 u
Number of unburnt muffins = 40 u

Total number of unburnt pastries
= 6 u + 40 u
= 46 u

46 u = 460

1 u = 460 ÷ 46 = 10

Number of unburnt banana muffins
= 5 u
= 5 x 10
= 50

(b)
Number of unburnt vanilla muffins
= 40 u - 5 u
= 35 u

^{Unburnt vanilla muffins}_{Total unburnt pastries}
= ³⁵_{6 + 40}
= ³⁵₄₆

Answer(s): (a) 50; (b) ³⁵₄₆