Esther, Shiyun, Lucy and Sarah went to buy a present for their mother. They shared the cost equally among themselves. However, Sarah forgot to bring her money. So, the other 3 girls paid for the present first. Lucy paid ³₅ of the amount Esther and Shiyun paid. Shiyun paid $12 more than Esther. The next day, Sarah returned $16 to Lucy and some money to Esther and Shiyun. How much did Sarah return to

1. Esther?
2. Shiyun?

	Esther	Shiyun	Lucy	Sarah	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 + 12
Amounts that each girl paid for Sarah first	- ?	- ?	- 16	+ 16 + ?
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 Lucy paid 
= 3 u - 2 u
= 1 u

1 u = 16

Total amount that Esther and Shiyun paid at first
= 5 u
= 5 x 16
= $80

1 p + 1 p + 12 = 80
2 p = 80 - 12
2 p = 68

1 p = 68 ÷ 2 = 34

Amount that Sarah needed to pay Esther
= 1 p - 2 u
= 34 - 2 x 16
= 34 - 32
= $2

(b)
Amount that Sarah needed to pay Shiyun
= (1 p + 12) - 2 u
= (34 + 12) - 2 x 16
= 46 - 32
= $14

Answer(s): (a) $2; (b) $14