Valen had some blueberry macarons and apple macarons. ³₁₀ of the number of blueberry macarons was equal to ¹₄ of the number of apple macarons. After Valen made 180 more blueberry macarons, the number of blueberry macarons was ⁷₃ of the number of apple macarons. How many macarons did he have altogether in the end?
Make the numerators the same. LCM of 3 and 1 is 3.

310 of blueberry macarons = 1x34x3 of apple macarons

³₁₀ of blueberry macarons = ³₁₂ of apple macarons

	Blueberry macarons	Apple macarons	Total
Before	10 u	12 u
Change	+ 180
After	7x4 = 28 u	3x4 = 12 u	40 u

The number of apple macarons remains unchanged.  Make the number of apple macarons the same.  LCM of 3 and 12 is 12.

Number of more blueberry macarons made
= 28 u - 10 u
= 18 u

18 u = 180

1 u = 180 ÷ 18 = 10

Number of macarons that Valen had in the end
= 28 u + 12 u
= 40 u
= 40 x 10
= 400

Answer(s): 400