Vincent had some chocolate chip shortbreads and blueberry shortbreads. ⁵₉ of the number of chocolate chip shortbreads was equal to ¹₅ of the number of blueberry shortbreads. After Vincent made 77 more chocolate chip shortbreads, the number of chocolate chip shortbreads was ⁴₅ of the number of blueberry shortbreads. How many shortbreads did he have altogether in the end?
Make the numerators the same. LCM of 5 and 1 is 5.

59 of chocolate chip shortbreads = 1x55x5 of blueberry shortbreads

⁵₉ of chocolate chip shortbreads = ⁵₂₅ of blueberry shortbreads

	Chocolate chip shortbreads	Blueberry shortbreads	Total
Before	9 u	25 u
Change	+ 77
After	4x5 = 20 u	5x5 = 25 u	45 u

The number of blueberry shortbreads remains unchanged.  Make the number of blueberry shortbreads the same.  LCM of 5 and 25 is 25.

Number of more chocolate chip shortbreads made
= 20 u - 9 u
= 11 u

11 u = 77

1 u = 77 ÷ 11 = 7

Number of shortbreads that Vincent had in the end
= 20 u + 25 u
= 45 u
= 45 x 7
= 315

Answer(s): 315