Risa, Esther, Anna and Elyse went to buy a gift for their grandmother. They shared the cost equally among themselves. However, Elyse forgot to bring her money. So, the other 3 girls paid for the gift first. Anna paid ³₅ of the amount Risa and Esther paid. Esther paid $7 more than Risa. The next day, Elyse returned $11 to Anna and some money to Risa and Esther. How much did Elyse return to

1. Risa?
2. Esther?

	Risa	Esther	Anna	Elyse	Total
Comparing the amounts 3 girls paid first	5 u		3 u		8 u
Comparing the amounts 2 girls paid first	1 p	1 p + 7
Amounts that each girl paid for Elyse first	- ?	- ?	- 11	+ 11 + ?
Comparing the amounts each girl should pay	1x2 = 2 u	1x2 = 2 u	1x2 = 2 u	1x2 = 2 u	4x2 = 8 u

(a)
The total amount that the 4 girls paid is repeated. Make the total amount the same.  LCM of 4 and 8 is 8.

Extra amount that Anna paid 
= 3 u - 2 u
= 1 u

1 u = 11

Total amount that Risa and Esther paid at first
= 5 u
= 5 x 11
= $55

1 p + 1 p + 7 = 55
2 p = 55 - 7
2 p = 48

1 p = 48 ÷ 2 = 24

Amount that Elyse needed to pay Risa
= 1 p - 2 u
= 24 - 2 x 11
= 24 - 22
= $2

(b)
Amount that Elyse needed to pay Esther
= (1 p + 7) - 2 u
= (24 + 7) - 2 x 11
= 31 - 22
= $9

Answer(s): (a) $2; (b) $9