Erika baked 70 macarons and wafers. She burnt 13 pieces and counted the remaining pieces. ¹₃ of the wafers and ⁷₈ of the macarons were cheese flavoured. There were equal number of wafers and macarons that were banana flavoured.

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

(a)
Number of pastries that was not burnt
= 70 - 13
= 57

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

Fraction of the macarons that was banana flavoured
= 1 - ⁷₈ 
= ¹₈ 

The number of banana wafers and banana macarons was the same. Make the numerators the same. 
23 Wafers = 1x28x2 Macarons 
23 Wafers = 216 Macarons 

Number of unburnt wafers = 3 u
Number of unburnt macarons = 16 u

Total number of unburnt pastries
= 3 u + 16 u
= 19 u

19 u = 57

1 u = 57 ÷ 19 = 3

Number of unburnt banana macarons
= 2 u
= 2 x 3
= 6

(b)
Number of unburnt cheese macarons
= 16 u - 2 u
= 14 u

^{Unburnt cheese macarons}_{Total unburnt pastries}
= ¹⁴_{3 + 16}
= ¹⁴₁₉

Answer(s): (a) 6; (b) ¹⁴₁₉