Three women, Xandra, Lynn and Linda went on a shopping spree. 90% of Xandra's spending was equal to ¹₆ of Lynn's spending. Linda's spending was  80% less than Lynn's. If Lynn spent $7776 less, she would spend the same amount of money as Linda.

1. Find the ratio of Xandra's spending to Lynn's to Linda's.
2. How much did Linda spend?

Xandra	Lynn	Linda
5x5	27x5
	5x27	1x27
25 u	135 u	27 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Xandra's spending is equal to ¹₆ of Lynn's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Xandra's spending = 16 of Lynn's spending
910 of Xandra's spending =1x96x9 of Lynn's spending
910 of Xandra's spending = 954 of Lynn's spending

Xandra : Lynn
10 : 54
5 : 27

Linda's spending in percent when compared to Lynn's
= 100% - 80%
= 20%

Lynn : Linda
100 : 20
5 : 1

Lynn's spending is the repeated identity.  Make Lynn's spending the same.  LCM of 27 and 5 is 135.

Xandra : Lynn : Linda
25 : 135 : 27

(b)

	Xandra	Lynn	Linda
Before	25 u	135 u	27 u
Change		- 108 u
After	25 u	27 u	27 u

Additional amount that Lynn would have to spend less to be the same as Linda
= 135 u - 27 u
= 108 u

108 u = 7776

1 u = 7776 ÷ 108 = 72

Amount that Linda spent
= 27 u
= 27 x 72
= $1944 

Answer(s): (a) 25 : 135 : 27; (b) $1944