Kylie and Barbara had 834 marbles altogether. They decided to play a game. In the first round, Barbara lost 50 marbles to Kylie. In the second round, Kylie lost 33 marbles to Barbara. At the end of the two rounds, Barbara had twice as many marbles as Kylie.

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

	Kylie	Barbara	Total
Before	1 u + 33 - 50	2 u - 33 + 50	834
Round 1	+ 50	- 50
Round 2	- 33	+ 33
After	1 u	2 u	834

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

3 u = 834

1 u = 834 ÷ 3 = 278

Number of marbles that Kylie had in the end
= 1 u
= 278

(b)
Working backwards.

Number of marbles that Barbara had at the end of round 2
= 2 u
= 2 x 278
= 556

Number of marbles that Barbara had at the end of round 1
= 556 - 33
= 523

Number of marbles that Barbara had at the beginning of the game
= 523 + 50
= 573

Answer(s): (a) 278; (b) 573