Xylia, Shannon, Jane and Vanessa went to buy a present for their cousin. They shared the cost equally among themselves. However, Vanessa forgot to bring her money. So, the other 3 girls paid for the present first. Jane paid ⁷₉ of the amount Xylia and Shannon paid. Shannon paid $5 more than Xylia. The next day, Vanessa returned $33 to Jane and some money to Xylia and Shannon. How much did Vanessa return to

1. Xylia?
2. Shannon?

	Xylia	Shannon	Jane	Vanessa	Total
Comparing the amounts 3 girls paid first	9 u		7 u		16 u
Comparing the amounts 2 girls paid first	1 p	1 p + 5
Amounts that each girl paid for Vanessa first	- ?	- ?	- 33	+ 33 + ?
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 Jane paid 
= 7 u - 4 u
= 3 u

3 u = 33

1 u = 33 ÷ 3 = 11

Total amount that Xylia and Shannon paid at first
= 9 u
= 9 x 11
= $99

1 p + 1 p + 5 = 99
2 p = 99 - 5
2 p = 94

1 p = 94 ÷ 2 = 47

Amount that Vanessa needed to pay Xylia
= 1 p - 4 u
= 47 - 4 x 11
= 47 - 44
= $3

(b)
Amount that Vanessa needed to pay Shannon
= (1 p + 5) - 4 u
= (47 + 5) - 4 x 11
= 52 - 44
= $8

Answer(s): (a) $3; (b) $8