Penelope, Yen, Jaslyn and Diana went to buy a souvenir for their father. They shared the cost equally among themselves. However, Diana forgot to bring her money. So, the other 3 girls paid for the souvenir first. Jaslyn paid ⁷₉ of the amount Penelope and Yen paid. Yen paid $6 more than Penelope. The next day, Diana returned $24 to Jaslyn and some money to Penelope and Yen. How much did Diana return to

1. Penelope?
2. Yen?

	Penelope	Yen	Jaslyn	Diana	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 + 6
Amounts that each girl paid for Diana first	- ?	- ?	- 24	+ 24 + ?
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 Jaslyn paid 
= 7 u - 4 u
= 3 u

3 u = 24

1 u = 24 ÷ 3 = 8

Total amount that Penelope and Yen paid at first
= 9 u
= 9 x 8
= $72

1 p + 1 p + 6 = 72
2 p = 72 - 6
2 p = 66

1 p = 66 ÷ 2 = 33

Amount that Diana needed to pay Penelope
= 1 p - 4 u
= 33 - 4 x 8
= 33 - 32
= $1

(b)
Amount that Diana needed to pay Yen
= (1 p + 6) - 4 u
= (33 + 6) - 4 x 8
= 39 - 32
= $7

Answer(s): (a) $1; (b) $7