Three women, Diana, Nora and Olivia went on a shopping spree. 70% of Diana's spending was equal to ¹₆ of Nora's spending. Olivia's spending was  25% less than Nora's. If Nora spent $1764 less, she would spend the same amount of money as Olivia.

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

Diana	Nora	Olivia
5x4	21x4
	4x21	3x21
20 u	84 u	63 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Diana's spending is equal to ¹₆ of Nora's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Diana's spending = 16 of Nora's spending
710 of Diana's spending =1x76x7 of Nora's spending
710 of Diana's spending = 742 of Nora's spending

Diana : Nora
10 : 42
5 : 21

Olivia's spending in percent when compared to Nora's
= 100% - 25%
= 75%

Nora : Olivia
100 : 75
4 : 3

Nora's spending is the repeated identity.  Make Nora's spending the same.  LCM of 21 and 4 is 84.

Diana : Nora : Olivia
20 : 84 : 63

(b)

	Diana	Nora	Olivia
Before	20 u	84 u	63 u
Change		- 21 u
After	20 u	63 u	63 u

Additional amount that Nora would have to spend less to be the same as Olivia
= 84 u - 63 u
= 21 u

21 u = 1764

1 u = 1764 ÷ 21 = 84

Amount that Olivia spent
= 63 u
= 63 x 84
= $5292 

Answer(s): (a) 20 : 84 : 63; (b) $5292