Victoria, Yoko, Nicole and Rachel went to buy a gift for their younger sister. They shared the cost equally among themselves. However, Rachel forgot to bring her money. So, the other 3 girls paid for the gift first. Nicole paid ⁵₁₁ of the amount Victoria and Yoko paid. Yoko paid $12 more than Victoria. The next day, Rachel returned $12 to Nicole and some money to Victoria and Yoko. How much did Rachel return to

1. Victoria?
2. Yoko?

	Victoria	Yoko	Nicole	Rachel	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 + 12
Amounts that each girl paid for Rachel first	- ?	- ?	- 12	+ 12 + ?
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 Nicole paid 
= 5 u - 4 u
= 1 u

1 u = 12

Total amount that Victoria and Yoko paid at first
= 11 u
= 11 x 12
= $132

1 p + 1 p + 12 = 132
2 p = 132 - 12
2 p = 120

1 p = 120 ÷ 2 = 60

Amount that Rachel needed to pay Victoria
= 1 p - 4 u
= 60 - 4 x 12
= 60 - 48
= $12

(b)
Amount that Rachel needed to pay Yoko
= (1 p + 12) - 4 u
= (60 + 12) - 4 x 12
= 72 - 48
= $24

Answer(s): (a) $12; (b) $24