Marion baked 78 biscuits and macarons. She burnt 6 pieces and counted the remaining pieces. ¹₃ of the macarons and ²₃ of the biscuits were cherry flavoured. There were equal number of macarons and biscuits that were cranberry flavoured.

1. How many unburnt cranberry biscuits were there?
2. What fraction of the unburnt pastries were cherry biscuits?

(a)
Number of pastries that was not burnt
= 78 - 6
= 72

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

Fraction of the biscuits that was cranberry flavoured
= 1 - ²₃ 
= ¹₃ 

The number of cranberry macarons and cranberry biscuits was the same. Make the numerators the same. 
23 Macarons = 1x23x2 Biscuits 
23 Macarons = 26 Biscuits 

Number of unburnt macarons = 3 u
Number of unburnt biscuits = 6 u

Total number of unburnt pastries
= 3 u + 6 u
= 9 u

9 u = 72

1 u = 72 ÷ 9 = 8

Number of unburnt cranberry biscuits
= 2 u
= 2 x 8
= 16

(b)
Number of unburnt cherry biscuits
= 6 u - 2 u
= 4 u

^{Unburnt cherry biscuits}_{Total unburnt pastries}
= ⁴_{3 + 6}
= ⁴₉

Answer(s): (a) 16; (b) ⁴₉