Kathy and Gabby had 890 buttons altogether. They decided to play a game. In the first round, Gabby lost 60 buttons to Kathy. In the second round, Kathy lost 31 buttons to Gabby. At the end of the two rounds, Gabby had four times as many buttons as Kathy.

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

	Kathy	Gabby	Total
Before	1 u + 31 - 60	4 u - 31 + 60	890
Round 1	+ 60	- 60
Round 2	- 31	+ 31
After	1 u	4 u	890

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

5 u = 890

1 u = 890 ÷ 5 = 178

Number of buttons that Kathy had in the end
= 1 u
= 178

(b)
Working backwards.

Number of buttons that Gabby had at the end of round 2
= 4 u
= 4 x 178
= 712

Number of buttons that Gabby had at the end of round 1
= 712 - 31
= 681

Number of buttons that Gabby had at the beginning of the game
= 681 + 60
= 741

Answer(s): (a) 178; (b) 741