Min, Penelope, Kathy and Sarah went to buy a gift for their grandfather. They shared the cost equally among themselves. However, Sarah forgot to bring her money. So, the other 3 girls paid for the gift first. Kathy paid ³₅ of the amount Min and Penelope paid. Penelope paid $2 more than Min. The next day, Sarah returned $4 to Kathy and some money to Min and Penelope. How much did Sarah return to

1. Min?
2. Penelope?

	Min	Penelope	Kathy	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 + 2
Amounts that each girl paid for Sarah first	- ?	- ?	- 4	+ 4 + ?
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 Kathy paid 
= 3 u - 2 u
= 1 u

1 u = 4

Total amount that Min and Penelope paid at first
= 5 u
= 5 x 4
= $20

1 p + 1 p + 2 = 20
2 p = 20 - 2
2 p = 18

1 p = 18 ÷ 2 = 9

Amount that Sarah needed to pay Min
= 1 p - 2 u
= 9 - 2 x 4
= 9 - 8
= $1

(b)
Amount that Sarah needed to pay Penelope
= (1 p + 2) - 2 u
= (9 + 2) - 2 x 4
= 11 - 8
= $3

Answer(s): (a) $1; (b) $3