Roshel, Natalie, Gem and Rachel went to buy a souvenir for their uncle. They shared the cost equally among themselves. However, Rachel forgot to bring her money. So, the other 3 girls paid for the souvenir first. Gem paid ⁷₉ of the amount Roshel and Natalie paid. Natalie paid $4 more than Roshel. The next day, Rachel returned $18 to Gem and some money to Roshel and Natalie. How much did Rachel return to

1. Roshel?
2. Natalie?

	Roshel	Natalie	Gem	Rachel	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 + 4
Amounts that each girl paid for Rachel first	- ?	- ?	- 18	+ 18 + ?
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 Gem paid 
= 7 u - 4 u
= 3 u

3 u = 18

1 u = 18 ÷ 3 = 6

Total amount that Roshel and Natalie paid at first
= 9 u
= 9 x 6
= $54

1 p + 1 p + 4 = 54
2 p = 54 - 4
2 p = 50

1 p = 50 ÷ 2 = 25

Amount that Rachel needed to pay Roshel
= 1 p - 4 u
= 25 - 4 x 6
= 25 - 24
= $1

(b)
Amount that Rachel needed to pay Natalie
= (1 p + 4) - 4 u
= (25 + 4) - 4 x 6
= 29 - 24
= $5

Answer(s): (a) $1; (b) $5