Ethan, Cody and Luis bought some macarons. After Ethan ate ⁵₈ of his macarons, Cody ate ⁴₅ of his macarons and Luis ate 11 macarons, each of them had the same number of macarons left. Ethan had 84 less macarons than Cody at first.

1. How many macarons did Ethan have at first?
2. How many macarons did the 3 of them buy altogether? 

	Ethan	Cody	Luis
Before	8 u	5x3 = 15 u	3 u + 11
Change	- 5 u	- 4x3 = - 12 u	- 11
After	3 u	1x3 = 3 u	3 u

(a)
The number of macarons that Ethan and Cody each had in the end is the same. Make the number of macarons that Ethan and Cody each had in the end the same.  LCM of 3 and 1 is 3.

Number of macarons that Ethan had less than Cody at first
= 15 u - 8 u
= 7 u

7 u = 84

1 u = 84 ÷ 7 = 12

Number of macarons that Ethan had at first
= 8 u
= 8 x 12
= 96 

(b)
Total number of macarons that the 3 of them bought
= 8 u + 15 u + 3 u + 11
= 26 u + 11
= 26 x 12 + 11
= 312 + 11
= 323

Answer(s): (a) 96; (b) 323