Xuan, Gem, Cindy and Anna went to buy a present for their auntie. They shared the cost equally among themselves. However, Anna forgot to bring her money. So, the other 3 girls paid for the present first. Cindy paid ³₅ of the amount Xuan and Gem paid. Gem paid $4 more than Xuan. The next day, Anna returned $12 to Cindy and some money to Xuan and Gem. How much did Anna return to

1. Xuan?
2. Gem?

	Xuan	Gem	Cindy	Anna	Total
Comparing the amounts 3 girls paid first	5 u		3 u		8 u
Comparing the amounts 2 girls paid first	1 p	1 p + 4
Amounts that each girl paid for Anna first	- ?	- ?	- 12	+ 12 + ?
Comparing the amounts each girl should pay	1x2 = 2 u	1x2 = 2 u	1x2 = 2 u	1x2 = 2 u	4x2 = 8 u

(a)
The total amount that the 4 girls paid is repeated. Make the total amount the same.  LCM of 4 and 8 is 8.

Extra amount that Cindy paid 
= 3 u - 2 u
= 1 u

1 u = 12

Total amount that Xuan and Gem paid at first
= 5 u
= 5 x 12
= $60

1 p + 1 p + 4 = 60
2 p = 60 - 4
2 p = 56

1 p = 56 ÷ 2 = 28

Amount that Anna needed to pay Xuan
= 1 p - 2 u
= 28 - 2 x 12
= 28 - 24
= $4

(b)
Amount that Anna needed to pay Gem
= (1 p + 4) - 2 u
= (28 + 4) - 2 x 12
= 32 - 24
= $8

Answer(s): (a) $4; (b) $8