Elyse baked 140 cookies and tarts. She burnt 17 pieces and counted the remaining pieces. ¹₆ of the tarts and ⁶₇ of the cookies were cherry flavoured. There were equal number of tarts and cookies that were cranberry flavoured.

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

(a)
Number of pastries that was not burnt
= 140 - 17
= 123

Fraction of the tarts that was cranberry flavoured
= 1 - ¹₆ 
= ⁵₆ 

Fraction of the cookies that was cranberry flavoured
= 1 - ⁶₇ 
= ¹₇ 

The number of cranberry tarts and cranberry cookies was the same. Make the numerators the same. 
56 Tarts = 1x57x5 Cookies 
56 Tarts = 535 Cookies 

Number of unburnt tarts = 6 u
Number of unburnt cookies = 35 u

Total number of unburnt pastries
= 6 u + 35 u
= 41 u

41 u = 123

1 u = 123 ÷ 41 = 3

Number of unburnt cranberry cookies
= 5 u
= 5 x 3
= 15

(b)
Number of unburnt cherry cookies
= 35 u - 5 u
= 30 u

^{Unburnt cherry cookies}_{Total unburnt pastries}
= ³⁰_{6 + 35}
= ³⁰₄₁

Answer(s): (a) 15; (b) ³⁰₄₁