Fanny and Nicole had 873 marbles altogether. They decided to play a game. In the first round, Nicole lost 52 marbles to Fanny. In the second round, Fanny lost 37 marbles to Nicole. At the end of the two rounds, Nicole had twice as many marbles as Fanny.

1. How many marbles did Fanny have in the end?
2. How many marbles did Nicole have at the beginning of the game?

	Fanny	Nicole	Total
Before	1 u + 37 - 52	2 u - 37 + 52	873
Round 1	+ 52	- 52
Round 2	- 37	+ 37
After	1 u	2 u	873

(a)
Total number of marbles
= 1 u + 2 u
= 3 u

3 u = 873

1 u = 873 ÷ 3 = 291

Number of marbles that Fanny had in the end
= 1 u
= 291

(b)
Working backwards.

Number of marbles that Nicole had at the end of round 2
= 2 u
= 2 x 291
= 582

Number of marbles that Nicole had at the end of round 1
= 582 - 37
= 545

Number of marbles that Nicole had at the beginning of the game
= 545 + 52
= 597

Answer(s): (a) 291; (b) 597