Shiyun, Esther, Roshel and Gwen went to buy a present for their auntie. They shared the cost equally among themselves. However, Gwen forgot to bring her money. So, the other 3 girls paid for the present first. Roshel paid ⁵₁₁ of the amount Shiyun and Esther paid. Esther paid $16 more than Shiyun. The next day, Gwen returned $16 to Roshel and some money to Shiyun and Esther. How much did Gwen return to

1. Shiyun?
2. Esther?

	Shiyun	Esther	Roshel	Gwen	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 + 16
Amounts that each girl paid for Gwen first	- ?	- ?	- 16	+ 16 + ?
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 Roshel paid 
= 5 u - 4 u
= 1 u

1 u = 16

Total amount that Shiyun and Esther paid at first
= 11 u
= 11 x 16
= $176

1 p + 1 p + 16 = 176
2 p = 176 - 16
2 p = 160

1 p = 160 ÷ 2 = 80

Amount that Gwen needed to pay Shiyun
= 1 p - 4 u
= 80 - 4 x 16
= 80 - 64
= $16

(b)
Amount that Gwen needed to pay Esther
= (1 p + 16) - 4 u
= (80 + 16) - 4 x 16
= 96 - 64
= $32

Answer(s): (a) $16; (b) $32