Three women, Kylie, Tina and Yoko went on a shopping spree. 70% of Kylie's spending was equal to ¹₆ of Tina's spending. Yoko's spending was  80% less than Tina's. If Tina spent $3528 less, she would spend the same amount of money as Yoko.

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

Kylie	Tina	Yoko
5x5	21x5
	5x21	1x21
25 u	105 u	21 u

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

710 of Kylie's spending = 16 of Tina's spending
710 of Kylie's spending =1x76x7 of Tina's spending
710 of Kylie's spending = 742 of Tina's spending

Kylie : Tina
10 : 42
5 : 21

Yoko's spending in percent when compared to Tina's
= 100% - 80%
= 20%

Tina : Yoko
100 : 20
5 : 1

Tina's spending is the repeated identity.  Make Tina's spending the same.  LCM of 21 and 5 is 105.

Kylie : Tina : Yoko
25 : 105 : 21

(b)

	Kylie	Tina	Yoko
Before	25 u	105 u	21 u
Change		- 84 u
After	25 u	21 u	21 u

Additional amount that Tina would have to spend less to be the same as Yoko
= 105 u - 21 u
= 84 u

84 u = 3528

1 u = 3528 ÷ 84 = 42

Amount that Yoko spent
= 21 u
= 21 x 42
= $882 

Answer(s): (a) 25 : 105 : 21; (b) $882