Sarah baked 114 biscuits and tarts. She burnt 19 pieces and counted the remaining pieces. ¹₃ of the tarts and ⁷₈ of the biscuits were banana flavoured. There were equal number of tarts and biscuits that were chocolate chip flavoured.

1. How many unburnt chocolate chip biscuits were there?
2. What fraction of the unburnt pastries were banana biscuits?

(a)
Number of pastries that was not burnt
= 114 - 19
= 95

Fraction of the tarts that was chocolate chip flavoured
= 1 - ¹₃ 
= ²₃ 

Fraction of the biscuits that was chocolate chip flavoured
= 1 - ⁷₈ 
= ¹₈ 

The number of chocolate chip tarts and chocolate chip biscuits was the same. Make the numerators the same. 
23 Tarts = 1x28x2 Biscuits 
23 Tarts = 216 Biscuits 

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

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

19 u = 95

1 u = 95 ÷ 19 = 5

Number of unburnt chocolate chip biscuits
= 2 u
= 2 x 5
= 10

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

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

Answer(s): (a) 10; (b) ¹⁴₁₉