Hilda baked 119 cookies and doughnuts. She burnt 11 pieces and counted the remaining pieces. ¹₃ of the doughnuts and ²₃ of the cookies were chocolate chip flavoured. There were equal number of doughnuts and cookies that were banana flavoured.

1. How many unburnt banana cookies were there?
2. What fraction of the unburnt pastries were chocolate chip cookies?

(a)
Number of pastries that was not burnt
= 119 - 11
= 108

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

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

The number of banana doughnuts and banana cookies was the same. Make the numerators the same. 
23 Doughnuts = 1x23x2 Cookies 
23 Doughnuts = 26 Cookies 

Number of unburnt doughnuts = 3 u
Number of unburnt cookies = 6 u

Total number of unburnt pastries
= 3 u + 6 u
= 9 u

9 u = 108

1 u = 108 ÷ 9 = 12

Number of unburnt banana cookies
= 2 u
= 2 x 12
= 24

(b)
Number of unburnt chocolate chip cookies
= 6 u - 2 u
= 4 u

^{Unburnt chocolate chip cookies}_{Total unburnt pastries}
= ⁴_{3 + 6}
= ⁴₉

Answer(s): (a) 24; (b) ⁴₉