Pierre has 90% as many marbles as Luke. If Pierre gives away 50% of the marbles and Luke gives away 20% of his marbles, they will have 225 marbles altogether. How many marbles do the two of them have?

	Pierre	Luke	Total
Comparing Pierre and Luke at first	9x2 = 18 u	10x2 = 20 u
Before	2x9 = 18 u	5x4 =  20 u
Change	- 1x9 = - 9 u	- 1x4 = - 4 u
After	1x9 = 9 u	4x4 = 16 u	225

90% = ⁹⁰₁₀₀ = ⁹₁₀

50% = ⁵⁰₁₀₀ = ¹₂ 

20% =²⁰₁₀₀ = ¹₅ 

The number of marbles that Pierre has at first is repeated.  Make the number of marbles that Pierre has the same.  LCM of 9 and 2 is 18 u.

The number of marbles that Luke has at first is repeated. Make the number of marbles that Luke has the same. LCM of 10 and 5 is 20 u.

Number of marbles in the end
= 9 u + 16 u
= 25 u

25 u = 225

1 u = 225 ÷ 25 = 9

Total number of marbles that the two of them have
= 18 u + 20 u
= 38 u
= 38 x 9
= 342

Answer(s): 342