Diana, Gem, Kathy and Lucy went to buy a souvenir for their older brother. They shared the cost equally among themselves. However, Lucy forgot to bring her money. So, the other 3 girls paid for the souvenir first. Kathy paid ⁵₁₁ of the amount Diana and Gem paid. Gem paid $13 more than Diana. The next day, Lucy returned $15 to Kathy and some money to Diana and Gem. How much did Lucy return to

1. Diana?
2. Gem?

	Diana	Gem	Kathy	Lucy	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 + 13
Amounts that each girl paid for Lucy 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 Kathy paid 
= 5 u - 4 u
= 1 u

1 u = 15

Total amount that Diana and Gem paid at first
= 11 u
= 11 x 15
= $165

1 p + 1 p + 13 = 165
2 p = 165 - 13
2 p = 152

1 p = 152 ÷ 2 = 76

Amount that Lucy needed to pay Diana
= 1 p - 4 u
= 76 - 4 x 15
= 76 - 60
= $16

(b)
Amount that Lucy needed to pay Gem
= (1 p + 13) - 4 u
= (76 + 13) - 4 x 15
= 89 - 60
= $29

Answer(s): (a) $16; (b) $29