Gem baked 150 puffs and muffins. She burnt 20 pieces and counted the remaining pieces. ¹₃ of the muffins and ⁴₅ of the puffs were cherry flavoured. There were equal number of muffins and puffs that were banana flavoured.

1. How many unburnt banana puffs were there?
2. What fraction of the unburnt pastries were cherry puffs?

(a)
Number of pastries that was not burnt
= 150 - 20
= 130

Fraction of the muffins that was banana flavoured
= 1 - ¹₃ 
= ²₃ 

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

The number of banana muffins and banana puffs was the same. Make the numerators the same. 
23 Muffins = 1x25x2 Puffs 
23 Muffins = 210 Puffs 

Number of unburnt muffins = 3 u
Number of unburnt puffs = 10 u

Total number of unburnt pastries
= 3 u + 10 u
= 13 u

13 u = 130

1 u = 130 ÷ 13 = 10

Number of unburnt banana puffs
= 2 u
= 2 x 10
= 20

(b)
Number of unburnt cherry puffs
= 10 u - 2 u
= 8 u

^{Unburnt cherry puffs}_{Total unburnt pastries}
= ⁸_{3 + 10}
= ⁸₁₃

Answer(s): (a) 20; (b) ⁸₁₃