Luke had some cranberry tarts and vanilla tarts. ²₃ of the number of cranberry tarts was equal to ¹₇ of the number of vanilla tarts. After Luke made 12 more cranberry tarts, the number of cranberry tarts was ¹₂ of the number of vanilla tarts. How many tarts did he have altogether in the end?
Make the numerators the same. LCM of 2 and 1 is 2.

23 of cranberry tarts = 1x27x2 of vanilla tarts

²₃ of cranberry tarts = ²₁₄ of vanilla tarts

	Cranberry tarts	Vanilla tarts	Total
Before	3 u	14 u
Change	+ 12
After	1x7 = 7 u	2x7 = 14 u	21 u

The number of vanilla tarts remains unchanged.  Make the number of vanilla tarts the same.  LCM of 2 and 14 is 14.

Number of more cranberry tarts made
= 7 u - 3 u
= 4 u

4 u = 12

1 u = 12 ÷ 4 = 3

Number of tarts that Luke had in the end
= 7 u + 14 u
= 21 u
= 21 x 3
= 63

Answer(s): 63