Luis had to paint some boxes. On the first day, the number of boxes he painted was 10% of the number of boxes that he had not painted. One week later, he painted another 289 boxes. As a result, the total number of painted boxes became 16 more than ⁴₅ of the total number of boxes. How many more boxes were unpainted than painted on the first day?

	Painted	Not painted	Total
Before	1x5 = 5 u	10x5 = 50 u	11x5 = 55 u
Change	+ 289	- 289
After	5 u + 289	50 u - 289	55 u
Comparing painted and not painted boxes in the end	4x11 + 16 = 44 u + 16	1x11 - 16 = 11 u - 16	5x11 = 55 u

10% = ¹⁰₁₀₀ = ¹₁₀
Painted : Not painted = 1 : 10

The total number of boxes remains unchanged. Make the total number of boxes at first and in the end the same.  LCM of 11 and 5 is 55.

The number of boxes painted in the end is repeated.

44 u + 16 = 5 u + 289
44 u - 5 u = 289 - 16
39 u = 273

1 u = 273 ÷ 39 = 7

Number of more boxes that were not painted than painted on the first day
= 50 u - 5 u
= 45 u
= 45 x 7
= 315

Answer(s): 315