Yen, Winnie, Natalie and Marion went to buy a gift for their younger sister. They shared the cost equally among themselves. However, Marion forgot to bring her money. So, the other 3 girls paid for the gift first. Natalie paid ⁵₁₁ of the amount Yen and Winnie paid. Winnie paid $17 more than Yen. The next day, Marion returned $7 to Natalie and some money to Yen and Winnie. How much did Marion return to

1. Yen?
2. Winnie?

	Yen	Winnie	Natalie	Marion	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 + 17
Amounts that each girl paid for Marion first	- ?	- ?	- 7	+ 7 + ?
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 Natalie paid 
= 5 u - 4 u
= 1 u

1 u = 7

Total amount that Yen and Winnie paid at first
= 11 u
= 11 x 7
= $77

1 p + 1 p + 17 = 77
2 p = 77 - 17
2 p = 60

1 p = 60 ÷ 2 = 30

Amount that Marion needed to pay Yen
= 1 p - 4 u
= 30 - 4 x 7
= 30 - 28
= $2

(b)
Amount that Marion needed to pay Winnie
= (1 p + 17) - 4 u
= (30 + 17) - 4 x 7
= 47 - 28
= $19

Answer(s): (a) $2; (b) $19