Diana baked 88 tarts and biscuits. She burnt 12 pieces and counted the remaining pieces. ¹₄ of the biscuits and ⁴₅ of the tarts were cherry flavoured. There were equal number of biscuits and tarts that were vanilla flavoured.

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

(a)
Number of pastries that was not burnt
= 88 - 12
= 76

Fraction of the biscuits that was vanilla flavoured
= 1 - ¹₄ 
= ³₄ 

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

The number of vanilla biscuits and vanilla tarts was the same. Make the numerators the same. 
34 Biscuits = 1x35x3 Tarts 
34 Biscuits = 315 Tarts 

Number of unburnt biscuits = 4 u
Number of unburnt tarts = 15 u

Total number of unburnt pastries
= 4 u + 15 u
= 19 u

19 u = 76

1 u = 76 ÷ 19 = 4

Number of unburnt vanilla tarts
= 3 u
= 3 x 4
= 12

(b)
Number of unburnt cherry tarts
= 15 u - 3 u
= 12 u

^{Unburnt cherry tarts}_{Total unburnt pastries}
= ¹²_{4 + 15}
= ¹²₁₉

Answer(s): (a) 12; (b) ¹²₁₉