Tina baked 190 scones and macarons. She burnt 3 pieces and counted the remaining pieces. ¹₃ of the macarons and ⁶₇ of the scones were cranberry flavoured. There were equal number of macarons and scones that were banana flavoured.

1. How many unburnt banana scones were there?
2. What fraction of the unburnt pastries were cranberry scones?

(a)
Number of pastries that was not burnt
= 190 - 3
= 187

Fraction of the macarons that was banana flavoured
= 1 - ¹₃ 
= ²₃ 

Fraction of the scones that was banana flavoured
= 1 - ⁶₇ 
= ¹₇ 

The number of banana macarons and banana scones was the same. Make the numerators the same. 
23 Macarons = 1x27x2 Scones 
23 Macarons = 214 Scones 

Number of unburnt macarons = 3 u
Number of unburnt scones = 14 u

Total number of unburnt pastries
= 3 u + 14 u
= 17 u

17 u = 187

1 u = 187 ÷ 17 = 11

Number of unburnt banana scones
= 2 u
= 2 x 11
= 22

(b)
Number of unburnt cranberry scones
= 14 u - 2 u
= 12 u

^{Unburnt cranberry scones}_{Total unburnt pastries}
= ¹²_{3 + 14}
= ¹²₁₇

Answer(s): (a) 22; (b) ¹²₁₇