Gillian baked 139 tarts and macarons. She burnt 14 pieces and counted the remaining pieces. ¹₅ of the macarons and ⁴₅ of the tarts were vanilla flavoured. There were equal number of macarons and tarts that were cranberry flavoured.

1. How many unburnt cranberry tarts were there?
2. What fraction of the unburnt pastries were vanilla tarts?

(a)
Number of pastries that was not burnt
= 139 - 14
= 125

Fraction of the macarons that was cranberry flavoured
= 1 - ¹₅ 
= ⁴₅ 

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

The number of cranberry macarons and cranberry tarts was the same. Make the numerators the same. 
45 Macarons = 1x45x4 Tarts 
45 Macarons = 420 Tarts 

Number of unburnt macarons = 5 u
Number of unburnt tarts = 20 u

Total number of unburnt pastries
= 5 u + 20 u
= 25 u

25 u = 125

1 u = 125 ÷ 25 = 5

Number of unburnt cranberry tarts
= 4 u
= 4 x 5
= 20

(b)
Number of unburnt vanilla tarts
= 20 u - 4 u
= 16 u

^{Unburnt vanilla tarts}_{Total unburnt pastries}
= ¹⁶_{5 + 20}
= ¹⁶₂₅

Answer(s): (a) 20; (b) ¹⁶₂₅