Tammy baked 98 cookies and cupcakes. She burnt 3 pieces and counted the remaining pieces. ¹₃ of the cupcakes and ⁷₈ of the cookies were banana flavoured. There were equal number of cupcakes and cookies that were vanilla flavoured.

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

(a)
Number of pastries that was not burnt
= 98 - 3
= 95

Fraction of the cupcakes that was vanilla flavoured
= 1 - ¹₃ 
= ²₃ 

Fraction of the cookies that was vanilla flavoured
= 1 - ⁷₈ 
= ¹₈ 

The number of vanilla cupcakes and vanilla cookies was the same. Make the numerators the same. 
23 Cupcakes = 1x28x2 Cookies 
23 Cupcakes = 216 Cookies 

Number of unburnt cupcakes = 3 u
Number of unburnt cookies = 16 u

Total number of unburnt pastries
= 3 u + 16 u
= 19 u

19 u = 95

1 u = 95 ÷ 19 = 5

Number of unburnt vanilla cookies
= 2 u
= 2 x 5
= 10

(b)
Number of unburnt banana cookies
= 16 u - 2 u
= 14 u

^{Unburnt banana cookies}_{Total unburnt pastries}
= ¹⁴_{3 + 16}
= ¹⁴₁₉

Answer(s): (a) 10; (b) ¹⁴₁₉