Betty, Xuan, Winnie and Gillian went to buy a gift for their cousin. They shared the cost equally among themselves. However, Gillian forgot to bring her money. So, the other 3 girls paid for the gift first. Winnie paid ⁵₁₁ of the amount Betty and Xuan paid. Xuan paid $8 more than Betty. The next day, Gillian returned $6 to Winnie and some money to Betty and Xuan. How much did Gillian return to

1. Betty?
2. Xuan?

	Betty	Xuan	Winnie	Gillian	Total
Comparing the amounts 3 girls paid first	11 u		5 u		16 u
Comparing the amounts 2 girls paid first	1 p	1 p + 8
Amounts that each girl paid for Gillian first	- ?	- ?	- 6	+ 6 + ?
Comparing the amounts each girl should pay	1x4 = 4 u	1x4 = 4 u	1x4 = 4 u	1x4 = 4 u	4x4 = 16 u

(a)
The total amount that the 4 girls paid is repeated. Make the total amount the same.  LCM of 4 and 16 is 16.

Extra amount that Winnie paid 
= 5 u - 4 u
= 1 u

1 u = 6

Total amount that Betty and Xuan paid at first
= 11 u
= 11 x 6
= $66

1 p + 1 p + 8 = 66
2 p = 66 - 8
2 p = 58

1 p = 58 ÷ 2 = 29

Amount that Gillian needed to pay Betty
= 1 p - 4 u
= 29 - 4 x 6
= 29 - 24
= $5

(b)
Amount that Gillian needed to pay Xuan
= (1 p + 8) - 4 u
= (29 + 8) - 4 x 6
= 37 - 24
= $13

Answer(s): (a) $5; (b) $13