Tammy, Barbara, Tiffany and Diana went to buy a gift for their younger sister. They shared the cost equally among themselves. However, Diana forgot to bring her money. So, the other 3 girls paid for the gift first. Tiffany paid ⁵₁₁ of the amount Tammy and Barbara paid. Barbara paid $5 more than Tammy. The next day, Diana returned $11 to Tiffany and some money to Tammy and Barbara. How much did Diana return to

1. Tammy?
2. Barbara?

	Tammy	Barbara	Tiffany	Diana	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 + 5
Amounts that each girl paid for Diana first	- ?	- ?	- 11	+ 11 + ?
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 = 11

Total amount that Tammy and Barbara paid at first
= 11 u
= 11 x 11
= $121

1 p + 1 p + 5 = 121
2 p = 121 - 5
2 p = 116

1 p = 116 ÷ 2 = 58

Amount that Diana needed to pay Tammy
= 1 p - 4 u
= 58 - 4 x 11
= 58 - 44
= $14

(b)
Amount that Diana needed to pay Barbara
= (1 p + 5) - 4 u
= (58 + 5) - 4 x 11
= 63 - 44
= $19

Answer(s): (a) $14; (b) $19