Three women, Shiyun, Yoko and Tammy went on a shopping spree. 70% of Shiyun's spending was equal to ¹₅ of Yoko's spending. Tammy's spending was  70% less than Yoko's. If Yoko spent $2597 less, she would spend the same amount of money as Tammy.

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

Shiyun	Yoko	Tammy
2x10	7x10
	10x7	3x7
20 u	70 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Shiyun's spending is equal to ¹₅ of Yoko's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Shiyun's spending = 15 of Yoko's spending
710 of Shiyun's spending =1x75x7 of Yoko's spending
710 of Shiyun's spending = 735 of Yoko's spending

Shiyun : Yoko
10 : 35
2 : 7

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

Yoko : Tammy
100 : 30
10 : 3

Yoko's spending is the repeated identity.  Make Yoko's spending the same.  LCM of 7 and 10 is 70.

Shiyun : Yoko : Tammy
20 : 70 : 21

(b)

	Shiyun	Yoko	Tammy
Before	20 u	70 u	21 u
Change		- 49 u
After	20 u	21 u	21 u

Additional amount that Yoko would have to spend less to be the same as Tammy
= 70 u - 21 u
= 49 u

49 u = 2597

1 u = 2597 ÷ 49 = 53

Amount that Tammy spent
= 21 u
= 21 x 53
= $1113 

Answer(s): (a) 20 : 70 : 21; (b) $1113