Kylie and Tiffany had 835 buttons altogether. They decided to play a game. In the first round, Tiffany lost 58 buttons to Kylie. In the second round, Kylie lost 36 buttons to Tiffany. At the end of the two rounds, Tiffany had four times as many buttons as Kylie.

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

	Kylie	Tiffany	Total
Before	1 u + 36 - 58	4 u - 36 + 58	835
Round 1	+ 58	- 58
Round 2	- 36	+ 36
After	1 u	4 u	835

(a)
Total number of buttons
= 1 u + 4 u
= 5 u

5 u = 835

1 u = 835 ÷ 5 = 167

Number of buttons that Kylie had in the end
= 1 u
= 167

(b)
Working backwards.

Number of buttons that Tiffany had at the end of round 2
= 4 u
= 4 x 167
= 668

Number of buttons that Tiffany had at the end of round 1
= 668 - 36
= 632

Number of buttons that Tiffany had at the beginning of the game
= 632 + 58
= 690

Answer(s): (a) 167; (b) 690