Shiyun, Penelope, Kylie and Opal went to buy a souvenir for their father. They shared the cost equally among themselves. However, Opal forgot to bring her money. So, the other 3 girls paid for the souvenir first. Kylie paid ³₅ of the amount Shiyun and Penelope paid. Penelope paid $13 more than Shiyun. The next day, Opal returned $15 to Kylie and some money to Shiyun and Penelope. How much did Opal return to

1. Shiyun?
2. Penelope?

	Shiyun	Penelope	Kylie	Opal	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 + 13
Amounts that each girl paid for Opal first	- ?	- ?	- 15	+ 15 + ?
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 Kylie paid 
= 3 u - 2 u
= 1 u

1 u = 15

Total amount that Shiyun and Penelope paid at first
= 5 u
= 5 x 15
= $75

1 p + 1 p + 13 = 75
2 p = 75 - 13
2 p = 62

1 p = 62 ÷ 2 = 31

Amount that Opal needed to pay Shiyun
= 1 p - 2 u
= 31 - 2 x 15
= 31 - 30
= $1

(b)
Amount that Opal needed to pay Penelope
= (1 p + 13) - 2 u
= (31 + 13) - 2 x 15
= 44 - 30
= $14

Answer(s): (a) $1; (b) $14