Three women, Yen, Esther and Joelle went on a shopping spree. 30% of Yen's spending was equal to ¹₅ of Esther's spending. Joelle's spending was  70% less than Esther's. If Esther spent $2058 less, she would spend the same amount of money as Joelle.

1. Find the ratio of Yen's spending to Esther's to Joelle's.
2. How much did Joelle spend?

Yen	Esther	Joelle
2x10	3x10
	10x3	3x3
20 u	30 u	9 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Yen's spending is equal to ¹₅ of Esther's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Yen's spending = 15 of Esther's spending
310 of Yen's spending =1x35x3 of Esther's spending
310 of Yen's spending = 315 of Esther's spending

Yen : Esther
10 : 15
2 : 3

Joelle's spending in percent when compared to Esther's
= 100% - 70%
= 30%

Esther : Joelle
100 : 30
10 : 3

Esther's spending is the repeated identity.  Make Esther's spending the same.  LCM of 3 and 10 is 30.

Yen : Esther : Joelle
20 : 30 : 9

(b)

	Yen	Esther	Joelle
Before	20 u	30 u	9 u
Change		- 21 u
After	20 u	9 u	9 u

Additional amount that Esther would have to spend less to be the same as Joelle
= 30 u - 9 u
= 21 u

21 u = 2058

1 u = 2058 ÷ 21 = 98

Amount that Joelle spent
= 9 u
= 9 x 98
= $882 

Answer(s): (a) 20 : 30 : 9; (b) $882