Ken had some cranberry tarts and apricot tarts. ³₁₀ of the number of cranberry tarts was equal to ¹₈ of the number of apricot tarts. After Ken made 460 more cranberry tarts, the number of cranberry tarts was ⁷₃ of the number of apricot tarts. How many tarts did he have altogether in the end?
Make the numerators the same. LCM of 3 and 1 is 3.

310 of cranberry tarts = 1x38x3 of apricot tarts

³₁₀ of cranberry tarts = ³₂₄ of apricot tarts

	Cranberry tarts	Apricot tarts	Total
Before	10 u	24 u
Change	+ 460
After	7x8 = 56 u	3x8 = 24 u	80 u

The number of apricot tarts remains unchanged.  Make the number of apricot tarts the same.  LCM of 3 and 24 is 24.

Number of more cranberry tarts made
= 56 u - 10 u
= 46 u

46 u = 460

1 u = 460 ÷ 46 = 10

Number of tarts that Ken had in the end
= 56 u + 24 u
= 80 u
= 80 x 10
= 800

Answer(s): 800