Jade baked 52 tarts and macarons. She burnt 4 pieces and counted the remaining pieces. ¹₄ of the macarons and ³₄ of the tarts were cheese flavoured. There were equal number of macarons and tarts that were apple flavoured.

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

(a)
Number of pastries that was not burnt
= 52 - 4
= 48

Fraction of the macarons that was apple flavoured
= 1 - ¹₄ 
= ³₄ 

Fraction of the tarts that was apple flavoured
= 1 - ³₄ 
= ¹₄ 

The number of apple macarons and apple tarts was the same. Make the numerators the same. 
34 Macarons = 1x34x3 Tarts 
34 Macarons = 312 Tarts 

Number of unburnt macarons = 4 u
Number of unburnt tarts = 12 u

Total number of unburnt pastries
= 4 u + 12 u
= 16 u

16 u = 48

1 u = 48 ÷ 16 = 3

Number of unburnt apple tarts
= 3 u
= 3 x 3
= 9

(b)
Number of unburnt cheese tarts
= 12 u - 3 u
= 9 u

^{Unburnt cheese tarts}_{Total unburnt pastries}
= ⁹_{4 + 12}
= ⁹₁₆

Answer(s): (a) 9; (b) ⁹₁₆