Fanny baked 231 doughnuts and cookies. She burnt 6 pieces and counted the remaining pieces. ¹₄ of the cookies and ⁶₇ of the doughnuts were cheese flavoured. There were equal number of cookies and doughnuts that were cranberry flavoured.

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

(a)
Number of pastries that was not burnt
= 231 - 6
= 225

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

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

The number of cranberry cookies and cranberry doughnuts was the same. Make the numerators the same. 
34 Cookies = 1x37x3 Doughnuts 
34 Cookies = 321 Doughnuts 

Number of unburnt cookies = 4 u
Number of unburnt doughnuts = 21 u

Total number of unburnt pastries
= 4 u + 21 u
= 25 u

25 u = 225

1 u = 225 ÷ 25 = 9

Number of unburnt cranberry doughnuts
= 3 u
= 3 x 9
= 27

(b)
Number of unburnt cheese doughnuts
= 21 u - 3 u
= 18 u

^{Unburnt cheese doughnuts}_{Total unburnt pastries}
= ¹⁸_{4 + 21}
= ¹⁸₂₅

Answer(s): (a) 27; (b) ¹⁸₂₅