Three women, Olivia, Yoko and Fanny went on a shopping spree. 30% of Olivia's spending was equal to ¹₆ of Yoko's spending. Fanny's spending was  70% less than Yoko's. If Yoko spent $4788 less, she would spend the same amount of money as Fanny.

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

Olivia	Yoko	Fanny
5x10	9x10
	10x9	3x9
50 u	90 u	27 u

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

310 of Olivia's spending = 16 of Yoko's spending
310 of Olivia's spending =1x36x3 of Yoko's spending
310 of Olivia's spending = 318 of Yoko's spending

Olivia : Yoko
10 : 18
5 : 9

Fanny's spending in percent when compared to Yoko's
= 100% - 70%
= 30%

Yoko : Fanny
100 : 30
10 : 3

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

Olivia : Yoko : Fanny
50 : 90 : 27

(b)

	Olivia	Yoko	Fanny
Before	50 u	90 u	27 u
Change		- 63 u
After	50 u	27 u	27 u

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

63 u = 4788

1 u = 4788 ÷ 63 = 76

Amount that Fanny spent
= 27 u
= 27 x 76
= $2052 

Answer(s): (a) 50 : 90 : 27; (b) $2052