Xylia, Lynn, Emily and Natalie went to buy a gift for their grandfather. They shared the cost equally among themselves. However, Natalie forgot to bring her money. So, the other 3 girls paid for the gift first. Emily paid ⁷₉ of the amount Xylia and Lynn paid. Lynn paid $6 more than Xylia. The next day, Natalie returned $30 to Emily and some money to Xylia and Lynn. How much did Natalie return to

1. Xylia?
2. Lynn?

	Xylia	Lynn	Emily	Natalie	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 + 6
Amounts that each girl paid for Natalie first	- ?	- ?	- 30	+ 30 + ?
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 Emily paid 
= 7 u - 4 u
= 3 u

3 u = 30

1 u = 30 ÷ 3 = 10

Total amount that Xylia and Lynn paid at first
= 9 u
= 9 x 10
= $90

1 p + 1 p + 6 = 90
2 p = 90 - 6
2 p = 84

1 p = 84 ÷ 2 = 42

Amount that Natalie needed to pay Xylia
= 1 p - 4 u
= 42 - 4 x 10
= 42 - 40
= $2

(b)
Amount that Natalie needed to pay Lynn
= (1 p + 6) - 4 u
= (42 + 6) - 4 x 10
= 48 - 40
= $8

Answer(s): (a) $2; (b) $8