Gem, Erika, Yen and Hilda went to buy a gift for their cousin. They shared the cost equally among themselves. However, Hilda forgot to bring her money. So, the other 3 girls paid for the gift first. Yen paid ⁷₉ of the amount Gem and Erika paid. Erika paid $5 more than Gem. The next day, Hilda returned $27 to Yen and some money to Gem and Erika. How much did Hilda return to

1. Gem?
2. Erika?

	Gem	Erika	Yen	Hilda	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 + 5
Amounts that each girl paid for Hilda first	- ?	- ?	- 27	+ 27 + ?
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 Yen paid 
= 7 u - 4 u
= 3 u

3 u = 27

1 u = 27 ÷ 3 = 9

Total amount that Gem and Erika paid at first
= 9 u
= 9 x 9
= $81

1 p + 1 p + 5 = 81
2 p = 81 - 5
2 p = 76

1 p = 76 ÷ 2 = 38

Amount that Hilda needed to pay Gem
= 1 p - 4 u
= 38 - 4 x 9
= 38 - 36
= $2

(b)
Amount that Hilda needed to pay Erika
= (1 p + 5) - 4 u
= (38 + 5) - 4 x 9
= 43 - 36
= $7

Answer(s): (a) $2; (b) $7