Shiyun, Sarah, Esther and Opal went to buy a souvenir for their older sister. They shared the cost equally among themselves. However, Opal forgot to bring her money. So, the other 3 girls paid for the souvenir first. Esther paid ⁵₁₁ of the amount Shiyun and Sarah paid. Sarah paid $20 more than Shiyun. The next day, Opal returned $18 to Esther and some money to Shiyun and Sarah. How much did Opal return to

1. Shiyun?
2. Sarah?

	Shiyun	Sarah	Esther	Opal	Total
Comparing the amounts 3 girls paid first	11 u		5 u		16 u
Comparing the amounts 2 girls paid first	1 p	1 p + 20
Amounts that each girl paid for Opal first	- ?	- ?	- 18	+ 18 + ?
Comparing the amounts each girl should pay	1x4 = 4 u	1x4 = 4 u	1x4 = 4 u	1x4 = 4 u	4x4 = 16 u

(a)
The total amount that the 4 girls paid is repeated. Make the total amount the same.  LCM of 4 and 16 is 16.

Extra amount that Esther paid 
= 5 u - 4 u
= 1 u

1 u = 18

Total amount that Shiyun and Sarah paid at first
= 11 u
= 11 x 18
= $198

1 p + 1 p + 20 = 198
2 p = 198 - 20
2 p = 178

1 p = 178 ÷ 2 = 89

Amount that Opal needed to pay Shiyun
= 1 p - 4 u
= 89 - 4 x 18
= 89 - 72
= $17

(b)
Amount that Opal needed to pay Sarah
= (1 p + 20) - 4 u
= (89 + 20) - 4 x 18
= 109 - 72
= $37

Answer(s): (a) $17; (b) $37