Xavier had some apple shortbreads and cherry shortbreads. ⁵₈ of the number of apple shortbreads was equal to ¹₆ of the number of cherry shortbreads. After Xavier made 100 more apple shortbreads, the number of apple shortbreads was ³₅ of the number of cherry shortbreads. How many shortbreads did he have altogether in the end?
Make the numerators the same. LCM of 5 and 1 is 5.

58 of apple shortbreads = 1x56x5 of cherry shortbreads

⁵₈ of apple shortbreads = ⁵₃₀ of cherry shortbreads

	Apple shortbreads	Cherry shortbreads	Total
Before	8 u	30 u
Change	+ 100
After	3x6 = 18 u	5x6 = 30 u	48 u

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

Number of more apple shortbreads made
= 18 u - 8 u
= 10 u

10 u = 100

1 u = 100 ÷ 10 = 10

Number of shortbreads that Xavier had in the end
= 18 u + 30 u
= 48 u
= 48 x 10
= 480

Answer(s): 480