Gem baked 163 doughnuts and cookies. She burnt 10 pieces and counted the remaining pieces. ¹₃ of the cookies and ⁶₇ of the doughnuts were blueberry flavoured. There were equal number of cookies and doughnuts that were cherry flavoured.

1. How many unburnt cherry doughnuts were there?
2. What fraction of the unburnt pastries were blueberry doughnuts?

(a)
Number of pastries that was not burnt
= 163 - 10
= 153

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

Fraction of the doughnuts that was cherry flavoured
= 1 - ⁶₇ 
= ¹₇ 

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

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

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

17 u = 153

1 u = 153 ÷ 17 = 9

Number of unburnt cherry doughnuts
= 2 u
= 2 x 9
= 18

(b)
Number of unburnt blueberry doughnuts
= 14 u - 2 u
= 12 u

^{Unburnt blueberry doughnuts}_{Total unburnt pastries}
= ¹²_{3 + 14}
= ¹²₁₇

Answer(s): (a) 18; (b) ¹²₁₇