Three women, Yoko, Esther and Tina went on a shopping spree. 30% of Yoko's spending was equal to ¹₅ of Esther's spending. Tina's spending was  40% less than Esther's. If Esther spent $426 less, she would spend the same amount of money as Tina.

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

Yoko	Esther	Tina
2x5	3x5
	5x3	3x3
10 u	15 u	9 u

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

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

Yoko : Esther
10 : 15
2 : 3

Tina's spending in percent when compared to Esther's
= 100% - 40%
= 60%

Esther : Tina
100 : 60
5 : 3

Esther's spending is the repeated identity.  Make Esther's spending the same.  LCM of 3 and 5 is 15.

Yoko : Esther : Tina
10 : 15 : 9

(b)

	Yoko	Esther	Tina
Before	10 u	15 u	9 u
Change		- 6 u
After	10 u	9 u	9 u

Additional amount that Esther would have to spend less to be the same as Tina
= 15 u - 9 u
= 6 u

6 u = 426

1 u = 426 ÷ 6 = 71

Amount that Tina spent
= 9 u
= 9 x 71
= $639 

Answer(s): (a) 10 : 15 : 9; (b) $639