Tammy, Victoria, Joelle and Rachel went to buy a gift for their grandmother. They shared the cost equally among themselves. However, Rachel forgot to bring her money. So, the other 3 girls paid for the gift first. Joelle paid ³₅ of the amount Tammy and Victoria paid. Victoria paid $13 more than Tammy. The next day, Rachel returned $17 to Joelle and some money to Tammy and Victoria. How much did Rachel return to

1. Tammy?
2. Victoria?

	Tammy	Victoria	Joelle	Rachel	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 Rachel first	- ?	- ?	- 17	+ 17 + ?
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 Joelle paid 
= 3 u - 2 u
= 1 u

1 u = 17

Total amount that Tammy and Victoria paid at first
= 5 u
= 5 x 17
= $85

1 p + 1 p + 13 = 85
2 p = 85 - 13
2 p = 72

1 p = 72 ÷ 2 = 36

Amount that Rachel needed to pay Tammy
= 1 p - 2 u
= 36 - 2 x 17
= 36 - 34
= $2

(b)
Amount that Rachel needed to pay Victoria
= (1 p + 13) - 2 u
= (36 + 13) - 2 x 17
= 49 - 34
= $15

Answer(s): (a) $2; (b) $15