Three women, Jaslyn, Penelope and Xuan went on a shopping spree. 30% of Jaslyn's spending was equal to ¹₆ of Penelope's spending. Xuan's spending was  70% less than Penelope's. If Penelope spent $6426 less, she would spend the same amount of money as Xuan.

1. Find the ratio of Jaslyn's spending to Penelope's to Xuan's.
2. How much did Xuan spend?

Jaslyn	Penelope	Xuan
5x10	9x10
	10x9	3x9
50 u	90 u	27 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Jaslyn's spending is equal to ¹₆ of Penelope's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Jaslyn's spending = 16 of Penelope's spending
310 of Jaslyn's spending =1x36x3 of Penelope's spending
310 of Jaslyn's spending = 318 of Penelope's spending

Jaslyn : Penelope
10 : 18
5 : 9

Xuan's spending in percent when compared to Penelope's
= 100% - 70%
= 30%

Penelope : Xuan
100 : 30
10 : 3

Penelope's spending is the repeated identity.  Make Penelope's spending the same.  LCM of 9 and 10 is 90.

Jaslyn : Penelope : Xuan
50 : 90 : 27

(b)

	Jaslyn	Penelope	Xuan
Before	50 u	90 u	27 u
Change		- 63 u
After	50 u	27 u	27 u

Additional amount that Penelope would have to spend less to be the same as Xuan
= 90 u - 27 u
= 63 u

63 u = 6426

1 u = 6426 ÷ 63 = 102

Amount that Xuan spent
= 27 u
= 27 x 102
= $2754 

Answer(s): (a) 50 : 90 : 27; (b) $2754