Rael had some banana cookies and cheese cookies. ²₇ of the number of banana cookies was equal to ¹₇ of the number of cheese cookies. After Rael made 336 more banana cookies, the number of banana cookies was ⁵₂ of the number of cheese cookies. How many cookies did he have altogether in the end?
Make the numerators the same. LCM of 2 and 1 is 2.

27 of banana cookies = 1x27x2 of cheese cookies

²₇ of banana cookies = ²₁₄ of cheese cookies

	Banana cookies	Cheese cookies	Total
Before	7 u	14 u
Change	+ 336
After	5x7 = 35 u	2x7 = 14 u	49 u

The number of cheese cookies remains unchanged.  Make the number of cheese cookies the same.  LCM of 2 and 14 is 14.

Number of more banana cookies made
= 35 u - 7 u
= 28 u

28 u = 336

1 u = 336 ÷ 28 = 12

Number of cookies that Rael had in the end
= 35 u + 14 u
= 49 u
= 49 x 12
= 588

Answer(s): 588