Daniel had some banana puffs and cherry puffs. ⁵₉ of the number of banana puffs was equal to ¹₃ of the number of cherry puffs. After Daniel made 30 more banana puffs, the number of banana puffs was ⁴₅ of the number of cherry puffs. How many puffs did he have altogether in the end?
Make the numerators the same. LCM of 5 and 1 is 5.

59 of banana puffs = 1x53x5 of cherry puffs

⁵₉ of banana puffs = ⁵₁₅ of cherry puffs

	Banana puffs	Cherry puffs	Total
Before	9 u	15 u
Change	+ 30
After	4x3 = 12 u	5x3 = 15 u	27 u

The number of cherry puffs remains unchanged.  Make the number of cherry puffs the same.  LCM of 5 and 15 is 15.

Number of more banana puffs made
= 12 u - 9 u
= 3 u

3 u = 30

1 u = 30 ÷ 3 = 10

Number of puffs that Daniel had in the end
= 12 u + 15 u
= 27 u
= 27 x 10
= 270

Answer(s): 270