Gillian baked 142 cookies and doughnuts. She burnt 6 pieces and counted the remaining pieces. ¹₃ of the doughnuts and ⁶₇ of the cookies were apple flavoured. There were equal number of doughnuts and cookies that were apricot flavoured.

1. How many unburnt apricot cookies were there?
2. What fraction of the unburnt pastries were apple cookies?

(a)
Number of pastries that was not burnt
= 142 - 6
= 136

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

Fraction of the cookies that was apricot flavoured
= 1 - ⁶₇ 
= ¹₇ 

The number of apricot doughnuts and apricot cookies was the same. Make the numerators the same. 
23 Doughnuts = 1x27x2 Cookies 
23 Doughnuts = 214 Cookies 

Number of unburnt doughnuts = 3 u
Number of unburnt cookies = 14 u

Total number of unburnt pastries
= 3 u + 14 u
= 17 u

17 u = 136

1 u = 136 ÷ 17 = 8

Number of unburnt apricot cookies
= 2 u
= 2 x 8
= 16

(b)
Number of unburnt apple cookies
= 14 u - 2 u
= 12 u

^{Unburnt apple cookies}_{Total unburnt pastries}
= ¹²_{3 + 14}
= ¹²₁₇

Answer(s): (a) 16; (b) ¹²₁₇