Fabian had some cheese tarts and cherry tarts. ⁵₉ of the number of cheese tarts was equal to ¹₆ of the number of cherry tarts. After Fabian made 45 more cheese tarts, the number of cheese tarts was ⁴₅ of the number of cherry tarts. How many tarts did he have altogether in the end?
Make the numerators the same. LCM of 5 and 1 is 5.

59 of cheese tarts = 1x56x5 of cherry tarts

⁵₉ of cheese tarts = ⁵₃₀ of cherry tarts

	Cheese tarts	Cherry tarts	Total
Before	9 u	30 u
Change	+ 45
After	4x6 = 24 u	5x6 = 30 u	54 u

The number of cherry tarts remains unchanged.  Make the number of cherry tarts the same.  LCM of 5 and 30 is 30.

Number of more cheese tarts made
= 24 u - 9 u
= 15 u

15 u = 45

1 u = 45 ÷ 15 = 3

Number of tarts that Fabian had in the end
= 24 u + 30 u
= 54 u
= 54 x 3
= 162

Answer(s): 162