Hilda baked 152 tarts and scones. She burnt 9 pieces and counted the remaining pieces. ¹₃ of the scones and ⁴₅ of the tarts were banana flavoured. There were equal number of scones and tarts that were cheese flavoured.

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

(a)
Number of pastries that was not burnt
= 152 - 9
= 143

Fraction of the scones that was cheese flavoured
= 1 - ¹₃ 
= ²₃ 

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

The number of cheese scones and cheese tarts was the same. Make the numerators the same. 
23 Scones = 1x25x2 Tarts 
23 Scones = 210 Tarts 

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

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

13 u = 143

1 u = 143 ÷ 13 = 11

Number of unburnt cheese tarts
= 2 u
= 2 x 11
= 22

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

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

Answer(s): (a) 22; (b) ⁸₁₃