Ben had some cranberry cookies and banana cookies. ³₈ of the number of cranberry cookies was equal to ¹₆ of the number of banana cookies. After Ben made 66 more cranberry cookies, the number of cranberry cookies was ⁵₃ of the number of banana cookies. How many cookies did he have altogether in the end?
Make the numerators the same. LCM of 3 and 1 is 3.

38 of cranberry cookies = 1x36x3 of banana cookies

³₈ of cranberry cookies = ³₁₈ of banana cookies

	Cranberry cookies	Banana cookies	Total
Before	8 u	18 u
Change	+ 66
After	5x6 = 30 u	3x6 = 18 u	48 u

The number of banana cookies remains unchanged.  Make the number of banana cookies the same.  LCM of 3 and 18 is 18.

Number of more cranberry cookies made
= 30 u - 8 u
= 22 u

22 u = 66

1 u = 66 ÷ 22 = 3

Number of cookies that Ben had in the end
= 30 u + 18 u
= 48 u
= 48 x 3
= 144

Answer(s): 144