Roshel, Jen, Tammy and Ivory went to buy a gift for their mother. They shared the cost equally among themselves. However, Ivory forgot to bring her money. So, the other 3 girls paid for the gift first. Tammy paid ⁵₁₁ of the amount Roshel and Jen paid. Jen paid $11 more than Roshel. The next day, Ivory returned $17 to Tammy and some money to Roshel and Jen. How much did Ivory return to

1. Roshel?
2. Jen?

	Roshel	Jen	Tammy	Ivory	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 + 11
Amounts that each girl paid for Ivory first	- ?	- ?	- 17	+ 17 + ?
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 Tammy paid 
= 5 u - 4 u
= 1 u

1 u = 17

Total amount that Roshel and Jen paid at first
= 11 u
= 11 x 17
= $187

1 p + 1 p + 11 = 187
2 p = 187 - 11
2 p = 176

1 p = 176 ÷ 2 = 88

Amount that Ivory needed to pay Roshel
= 1 p - 4 u
= 88 - 4 x 17
= 88 - 68
= $20

(b)
Amount that Ivory needed to pay Jen
= (1 p + 11) - 4 u
= (88 + 11) - 4 x 17
= 99 - 68
= $31

Answer(s): (a) $20; (b) $31