Olivia, Dana and Jean shared $450 among themselves. Dana and Jean shared ²₅ of the money equally. After Dana gave away some of her money to Olivia, Jean had 6 times as much money as Dana. How much money did Dana give to Olivia?

	Dana	Jean	Olivia	Total
Before	1x6 = 6 u	1x6 = 6 u	3x6 = 18 u	30 u
Change	- 5 u	No change	+ 5 u
After	1x1 = 1 u	6x1 = 6 u	23 u	30 u

Dana and Jean shared ²₅ of the money equally.

Fraction of the money that Dana and Jean each had
= ²₅ ÷ 2
= ²₅ x ¹₂
= ¹₅

The amount that Jean had remains unchanged.  The amount that Jean had is the unchanged quantity. Make the amount that Jean had the same. LCM of 1 and 6 is 6.

The amount that Dana and Jean had at first is the same.

Total amount that they had at first
= 6 u + 6 u + 18 u
= 30 u

30 u = 450

1 u = 450 ÷ 30 = 15

Amount that Dana gave to Olivia
= 6 u - 1 u
= 5 u
= 5 x 15
= $75

Answer(s): $75