Mary baked 165 macarons and scones. She burnt 17 pieces and counted the remaining pieces. ¹₅ of the scones and ⁷₈ of the macarons were banana flavoured. There were equal number of scones and macarons that were apricot flavoured.

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

(a)
Number of pastries that was not burnt
= 165 - 17
= 148

Fraction of the scones that was apricot flavoured
= 1 - ¹₅ 
= ⁴₅ 

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

The number of apricot scones and apricot macarons was the same. Make the numerators the same. 
45 Scones = 1x48x4 Macarons 
45 Scones = 432 Macarons 

Number of unburnt scones = 5 u
Number of unburnt macarons = 32 u

Total number of unburnt pastries
= 5 u + 32 u
= 37 u

37 u = 148

1 u = 148 ÷ 37 = 4

Number of unburnt apricot macarons
= 4 u
= 4 x 4
= 16

(b)
Number of unburnt banana macarons
= 32 u - 4 u
= 28 u

^{Unburnt banana macarons}_{Total unburnt pastries}
= ²⁸_{5 + 32}
= ²⁸₃₇

Answer(s): (a) 16; (b) ²⁸₃₇