Jean, Emily, Gabby and Kathy went to buy a present for their older sister. They shared the cost equally among themselves. However, Kathy forgot to bring her money. So, the other 3 girls paid for the present first. Gabby paid ⁵₁₁ of the amount Jean and Emily paid. Emily paid $4 more than Jean. The next day, Kathy returned $14 to Gabby and some money to Jean and Emily. How much did Kathy return to

1. Jean?
2. Emily?

	Jean	Emily	Gabby	Kathy	Total
Comparing the amounts 3 girls paid first	11 u		5 u		16 u
Comparing the amounts 2 girls paid first	1 p	1 p + 4
Amounts that each girl paid for Kathy first	- ?	- ?	- 14	+ 14 + ?
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 Gabby paid 
= 5 u - 4 u
= 1 u

1 u = 14

Total amount that Jean and Emily paid at first
= 11 u
= 11 x 14
= $154

1 p + 1 p + 4 = 154
2 p = 154 - 4
2 p = 150

1 p = 150 ÷ 2 = 75

Amount that Kathy needed to pay Jean
= 1 p - 4 u
= 75 - 4 x 14
= 75 - 56
= $19

(b)
Amount that Kathy needed to pay Emily
= (1 p + 4) - 4 u
= (75 + 4) - 4 x 14
= 79 - 56
= $23

Answer(s): (a) $19; (b) $23