Three women, Shiyun, Nicole and Zoe went on a shopping spree. 90% of Shiyun's spending was equal to ¹₆ of Nicole's spending. Zoe's spending was  25% less than Nicole's. If Nicole spent $2943 less, she would spend the same amount of money as Zoe.

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

Shiyun	Nicole	Zoe
5x4	27x4
	4x27	3x27
20 u	108 u	81 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Shiyun's spending is equal to ¹₆ of Nicole's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Shiyun's spending = 16 of Nicole's spending
910 of Shiyun's spending =1x96x9 of Nicole's spending
910 of Shiyun's spending = 954 of Nicole's spending

Shiyun : Nicole
10 : 54
5 : 27

Zoe's spending in percent when compared to Nicole's
= 100% - 25%
= 75%

Nicole : Zoe
100 : 75
4 : 3

Nicole's spending is the repeated identity.  Make Nicole's spending the same.  LCM of 27 and 4 is 108.

Shiyun : Nicole : Zoe
20 : 108 : 81

(b)

	Shiyun	Nicole	Zoe
Before	20 u	108 u	81 u
Change		- 27 u
After	20 u	81 u	81 u

Additional amount that Nicole would have to spend less to be the same as Zoe
= 108 u - 81 u
= 27 u

27 u = 2943

1 u = 2943 ÷ 27 = 109

Amount that Zoe spent
= 81 u
= 81 x 109
= $8829 

Answer(s): (a) 20 : 108 : 81; (b) $8829