Penelope, Emily, Tiffany and Cathy went to buy a souvenir for their grandmother. They shared the cost equally among themselves. However, Cathy forgot to bring her money. So, the other 3 girls paid for the souvenir first. Tiffany paid ⁵₁₁ of the amount Penelope and Emily paid. Emily paid $2 more than Penelope. The next day, Cathy returned $2 to Tiffany and some money to Penelope and Emily. How much did Cathy return to

1. Penelope?
2. Emily?

	Penelope	Emily	Tiffany	Cathy	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 + 2
Amounts that each girl paid for Cathy first	- ?	- ?	- 2	+ 2 + ?
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 Tiffany paid 
= 5 u - 4 u
= 1 u

1 u = 2

Total amount that Penelope and Emily paid at first
= 11 u
= 11 x 2
= $22

1 p + 1 p + 2 = 22
2 p = 22 - 2
2 p = 20

1 p = 20 ÷ 2 = 10

Amount that Cathy needed to pay Penelope
= 1 p - 4 u
= 10 - 4 x 2
= 10 - 8
= $2

(b)
Amount that Cathy needed to pay Emily
= (1 p + 2) - 4 u
= (10 + 2) - 4 x 2
= 12 - 8
= $4

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