Rael had some cherry macarons and cranberry macarons. ³₁₀ of the number of cherry macarons was equal to ¹₄ of the number of cranberry macarons. After Rael made 36 more cherry macarons, the number of cherry macarons was ⁷₃ of the number of cranberry 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 cherry macarons = 1x34x3 of cranberry macarons

³₁₀ of cherry macarons = ³₁₂ of cranberry macarons

	Cherry macarons	Cranberry macarons	Total
Before	10 u	12 u
Change	+ 36
After	7x4 = 28 u	3x4 = 12 u	40 u

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

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

18 u = 36

1 u = 36 ÷ 18 = 2

Number of macarons that Rael had in the end
= 28 u + 12 u
= 40 u
= 40 x 2
= 80

Answer(s): 80