Olivia, Shannon, Ivory and Jane went to buy a souvenir for their younger sister. They shared the cost equally among themselves. However, Jane forgot to bring her money. So, the other 3 girls paid for the souvenir first. Ivory paid ⁵₁₁ of the amount Olivia and Shannon paid. Shannon paid $17 more than Olivia. The next day, Jane returned $13 to Ivory and some money to Olivia and Shannon. How much did Jane return to

1. Olivia?
2. Shannon?

	Olivia	Shannon	Ivory	Jane	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 + 17
Amounts that each girl paid for Jane first	- ?	- ?	- 13	+ 13 + ?
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 Ivory paid 
= 5 u - 4 u
= 1 u

1 u = 13

Total amount that Olivia and Shannon paid at first
= 11 u
= 11 x 13
= $143

1 p + 1 p + 17 = 143
2 p = 143 - 17
2 p = 126

1 p = 126 ÷ 2 = 63

Amount that Jane needed to pay Olivia
= 1 p - 4 u
= 63 - 4 x 13
= 63 - 52
= $11

(b)
Amount that Jane needed to pay Shannon
= (1 p + 17) - 4 u
= (63 + 17) - 4 x 13
= 80 - 52
= $28

Answer(s): (a) $11; (b) $28