Esther baked 232 scones and tarts. She burnt 4 pieces and counted the remaining pieces. ¹₃ of the tarts and ⁷₈ of the scones were cheese flavoured. There were equal number of tarts and scones that were apple flavoured.

1. How many unburnt apple scones were there?
2. What fraction of the unburnt pastries were cheese scones?

(a)
Number of pastries that was not burnt
= 232 - 4
= 228

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

Fraction of the scones that was apple flavoured
= 1 - ⁷₈ 
= ¹₈ 

The number of apple tarts and apple scones was the same. Make the numerators the same. 
23 Tarts = 1x28x2 Scones 
23 Tarts = 216 Scones 

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

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

19 u = 228

1 u = 228 ÷ 19 = 12

Number of unburnt apple scones
= 2 u
= 2 x 12
= 24

(b)
Number of unburnt cheese scones
= 16 u - 2 u
= 14 u

^{Unburnt cheese scones}_{Total unburnt pastries}
= ¹⁴_{3 + 16}
= ¹⁴₁₉

Answer(s): (a) 24; (b) ¹⁴₁₉