Fiona baked 169 puffs and tarts. She burnt 13 pieces and counted the remaining pieces. ¹₄ of the tarts and ²₃ of the puffs were cheese flavoured. There were equal number of tarts and puffs that were cranberry flavoured.

1. How many unburnt cranberry puffs were there?
2. What fraction of the unburnt pastries were cheese puffs?

(a)
Number of pastries that was not burnt
= 169 - 13
= 156

Fraction of the tarts that was cranberry flavoured
= 1 - ¹₄ 
= ³₄ 

Fraction of the puffs that was cranberry flavoured
= 1 - ²₃ 
= ¹₃ 

The number of cranberry tarts and cranberry puffs was the same. Make the numerators the same. 
34 Tarts = 1x33x3 Puffs 
34 Tarts = 39 Puffs 

Number of unburnt tarts = 4 u
Number of unburnt puffs = 9 u

Total number of unburnt pastries
= 4 u + 9 u
= 13 u

13 u = 156

1 u = 156 ÷ 13 = 12

Number of unburnt cranberry puffs
= 3 u
= 3 x 12
= 36

(b)
Number of unburnt cheese puffs
= 9 u - 3 u
= 6 u

^{Unburnt cheese puffs}_{Total unburnt pastries}
= ⁶_{4 + 9}
= ⁶₁₃

Answer(s): (a) 36; (b) ⁶₁₃