Xandra baked 87 cupcakes and cookies. She burnt 10 pieces and counted the remaining pieces. ¹₃ of the cookies and ³₄ of the cupcakes were cheese flavoured. There were equal number of cookies and cupcakes that were cherry flavoured.

1. How many unburnt cherry cupcakes were there?
2. What fraction of the unburnt pastries were cheese cupcakes?

(a)
Number of pastries that was not burnt
= 87 - 10
= 77

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

Fraction of the cupcakes that was cherry flavoured
= 1 - ³₄ 
= ¹₄ 

The number of cherry cookies and cherry cupcakes was the same. Make the numerators the same. 
23 Cookies = 1x24x2 Cupcakes 
23 Cookies = 28 Cupcakes 

Number of unburnt cookies = 3 u
Number of unburnt cupcakes = 8 u

Total number of unburnt pastries
= 3 u + 8 u
= 11 u

11 u = 77

1 u = 77 ÷ 11 = 7

Number of unburnt cherry cupcakes
= 2 u
= 2 x 7
= 14

(b)
Number of unburnt cheese cupcakes
= 8 u - 2 u
= 6 u

^{Unburnt cheese cupcakes}_{Total unburnt pastries}
= ⁶_{3 + 8}
= ⁶₁₁

Answer(s): (a) 14; (b) ⁶₁₁