Three women, Shiyun, Tammy and Jean went on a shopping spree. 70% of Shiyun's spending was equal to ¹₅ of Tammy's spending. Jean's spending was  60% more than Tammy's. If Tammy spent another $1197, she would spend the same amount of money as Jean.

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

Shiyun	Tammy	Jean
2x5	7x5
	5x7	8x7
10 u	35 u	56 u

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

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

Shiyun : Tammy
10 : 35
2 : 7

Jean's spending in percent when compared to Tammy's
= 100% + 60%
= 160%

Tammy : Jean
100 : 160
5 : 8

Tammy's spending is the repeated identity.  Make Tammy's spending the same.  LCM of 7 and 5 is 35.

Shiyun : Tammy : Jean
10 : 35 : 56

(b)

	Shiyun	Tammy	Jean
Before	10 u	35 u	56 u
Change		+ 21 u
After	10 u	56 u	56 u

Additional amount that Tammy would have to spend to be the same as Jean
= 56 u - 35 u
= 21 u

21 u = 1197

1 u = 1197 ÷ 21 = 57

Amount that Shiyun spent
= 10 u
= 10 x 57
= $570 

Answer(s): (a) 10 : 35 : 56; (b) $570