Three women, Shiyun, Ivory and Lucy went on a shopping spree. 70% of Shiyun's spending was equal to ¹₂ of Ivory's spending. Lucy's spending was  25% less than Ivory's. If Ivory spent $224 less, she would spend the same amount of money as Lucy.

1. Find the ratio of Shiyun's spending to Ivory's to Lucy's.
2. How much did Lucy spend?

Shiyun	Ivory	Lucy
5x4	7x4
	4x7	3x7
20 u	28 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Shiyun's spending is equal to ¹₂ of Ivory's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Shiyun's spending = 12 of Ivory's spending
710 of Shiyun's spending =1x72x7 of Ivory's spending
710 of Shiyun's spending = 714 of Ivory's spending

Shiyun : Ivory
10 : 14
5 : 7

Lucy's spending in percent when compared to Ivory's
= 100% - 25%
= 75%

Ivory : Lucy
100 : 75
4 : 3

Ivory's spending is the repeated identity.  Make Ivory's spending the same.  LCM of 7 and 4 is 28.

Shiyun : Ivory : Lucy
20 : 28 : 21

(b)

	Shiyun	Ivory	Lucy
Before	20 u	28 u	21 u
Change		- 7 u
After	20 u	21 u	21 u

Additional amount that Ivory would have to spend less to be the same as Lucy
= 28 u - 21 u
= 7 u

7 u = 224

1 u = 224 ÷ 7 = 32

Amount that Lucy spent
= 21 u
= 21 x 32
= $672 

Answer(s): (a) 20 : 28 : 21; (b) $672