Rachel, Lucy, Joelle and Sarah went to buy a souvenir for their auntie. They shared the cost equally among themselves. However, Sarah forgot to bring her money. So, the other 3 girls paid for the souvenir first. Joelle paid ³₅ of the amount Rachel and Lucy paid. Lucy paid $3 more than Rachel. The next day, Sarah returned $7 to Joelle and some money to Rachel and Lucy. How much did Sarah return to

1. Rachel?
2. Lucy?

	Rachel	Lucy	Joelle	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 + 3
Amounts that each girl paid for Sarah first	- ?	- ?	- 7	+ 7 + ?
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 Joelle paid 
= 3 u - 2 u
= 1 u

1 u = 7

Total amount that Rachel and Lucy paid at first
= 5 u
= 5 x 7
= $35

1 p + 1 p + 3 = 35
2 p = 35 - 3
2 p = 32

1 p = 32 ÷ 2 = 16

Amount that Sarah needed to pay Rachel
= 1 p - 2 u
= 16 - 2 x 7
= 16 - 14
= $2

(b)
Amount that Sarah needed to pay Lucy
= (1 p + 3) - 2 u
= (16 + 3) - 2 x 7
= 19 - 14
= $5

Answer(s): (a) $2; (b) $5