Jen baked 47 tarts and cupcakes. She burnt 9 pieces and counted the remaining pieces. ¹₃ of the cupcakes and ⁷₈ of the tarts were blueberry flavoured. There were equal number of cupcakes and tarts that were strawberry flavoured.

1. How many unburnt strawberry tarts were there?
2. What fraction of the unburnt pastries were blueberry tarts?

(a)
Number of pastries that was not burnt
= 47 - 9
= 38

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

Fraction of the tarts that was strawberry flavoured
= 1 - ⁷₈ 
= ¹₈ 

The number of strawberry cupcakes and strawberry tarts was the same. Make the numerators the same. 
23 Cupcakes = 1x28x2 Tarts 
23 Cupcakes = 216 Tarts 

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

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

19 u = 38

1 u = 38 ÷ 19 = 2

Number of unburnt strawberry tarts
= 2 u
= 2 x 2
= 4

(b)
Number of unburnt blueberry tarts
= 16 u - 2 u
= 14 u

^{Unburnt blueberry tarts}_{Total unburnt pastries}
= ¹⁴_{3 + 16}
= ¹⁴₁₉

Answer(s): (a) 4; (b) ¹⁴₁₉