Emma, Diana, Cindy and Emily went to buy a present for their auntie. They shared the cost equally among themselves. However, Emily forgot to bring her money. So, the other 3 girls paid for the present first. Cindy paid ⁷₉ of the amount Emma and Diana paid. Diana paid $2 more than Emma. The next day, Emily returned $18 to Cindy and some money to Emma and Diana. How much did Emily return to

1. Emma?
2. Diana?

	Emma	Diana	Cindy	Emily	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 + 2
Amounts that each girl paid for Emily 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 Cindy paid 
= 7 u - 4 u
= 3 u

3 u = 18

1 u = 18 ÷ 3 = 6

Total amount that Emma and Diana paid at first
= 9 u
= 9 x 6
= $54

1 p + 1 p + 2 = 54
2 p = 54 - 2
2 p = 52

1 p = 52 ÷ 2 = 26

Amount that Emily needed to pay Emma
= 1 p - 4 u
= 26 - 4 x 6
= 26 - 24
= $2

(b)
Amount that Emily needed to pay Diana
= (1 p + 2) - 4 u
= (26 + 2) - 4 x 6
= 28 - 24
= $4

Answer(s): (a) $2; (b) $4