Xandra, Gillian, Victoria and Rachel went to buy a souvenir for their grandfather. They shared the cost equally among themselves. However, Rachel forgot to bring her money. So, the other 3 girls paid for the souvenir first. Victoria paid ⁷₉ of the amount Xandra and Gillian paid. Gillian paid $8 more than Xandra. The next day, Rachel returned $30 to Victoria and some money to Xandra and Gillian. How much did Rachel return to

1. Xandra?
2. Gillian?

	Xandra	Gillian	Victoria	Rachel	Total
Comparing the amounts 3 girls paid first	9 u		7 u		16 u
Comparing the amounts 2 girls paid first	1 p	1 p + 8
Amounts that each girl paid for Rachel first	- ?	- ?	- 30	+ 30 + ?
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 Victoria paid 
= 7 u - 4 u
= 3 u

3 u = 30

1 u = 30 ÷ 3 = 10

Total amount that Xandra and Gillian paid at first
= 9 u
= 9 x 10
= $90

1 p + 1 p + 8 = 90
2 p = 90 - 8
2 p = 82

1 p = 82 ÷ 2 = 41

Amount that Rachel needed to pay Xandra
= 1 p - 4 u
= 41 - 4 x 10
= 41 - 40
= $1

(b)
Amount that Rachel needed to pay Gillian
= (1 p + 8) - 4 u
= (41 + 8) - 4 x 10
= 49 - 40
= $9

Answer(s): (a) $1; (b) $9