Rachel, Zara, Yen and Abi went to buy a gift for their uncle. They shared the cost equally among themselves. However, Abi forgot to bring her money. So, the other 3 girls paid for the gift first. Yen paid ⁷₉ of the amount Rachel and Zara paid. Zara paid $3 more than Rachel. The next day, Abi returned $15 to Yen and some money to Rachel and Zara. How much did Abi return to

1. Rachel?
2. Zara?

	Rachel	Zara	Yen	Abi	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 + 3
Amounts that each girl paid for Abi first	- ?	- ?	- 15	+ 15 + ?
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 Yen paid 
= 7 u - 4 u
= 3 u

3 u = 15

1 u = 15 ÷ 3 = 5

Total amount that Rachel and Zara paid at first
= 9 u
= 9 x 5
= $45

1 p + 1 p + 3 = 45
2 p = 45 - 3
2 p = 42

1 p = 42 ÷ 2 = 21

Amount that Abi needed to pay Rachel
= 1 p - 4 u
= 21 - 4 x 5
= 21 - 20
= $1

(b)
Amount that Abi needed to pay Zara
= (1 p + 3) - 4 u
= (21 + 3) - 4 x 5
= 24 - 20
= $4

Answer(s): (a) $1; (b) $4