Julie baked 93 tarts and biscuits. She burnt 15 pieces and counted the remaining pieces. ¹₃ of the biscuits and ⁴₅ of the tarts were cheese flavoured. There were equal number of biscuits and tarts that were cherry flavoured.

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

(a)
Number of pastries that was not burnt
= 93 - 15
= 78

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

Fraction of the tarts that was cherry flavoured
= 1 - ⁴₅ 
= ¹₅ 

The number of cherry biscuits and cherry tarts was the same. Make the numerators the same. 
23 Biscuits = 1x25x2 Tarts 
23 Biscuits = 210 Tarts 

Number of unburnt biscuits = 3 u
Number of unburnt tarts = 10 u

Total number of unburnt pastries
= 3 u + 10 u
= 13 u

13 u = 78

1 u = 78 ÷ 13 = 6

Number of unburnt cherry tarts
= 2 u
= 2 x 6
= 12

(b)
Number of unburnt cheese tarts
= 10 u - 2 u
= 8 u

^{Unburnt cheese tarts}_{Total unburnt pastries}
= ⁸_{3 + 10}
= ⁸₁₃

Answer(s): (a) 12; (b) ⁸₁₃