Three women, Min, Anna and Yen went on a shopping spree. 70% of Min's spending was equal to ¹₅ of Anna's spending. Yen's spending was  70% less than Anna's. If Anna spent $3087 less, she would spend the same amount of money as Yen.

1. Find the ratio of Min's spending to Anna's to Yen's.
2. How much did Yen spend?

Min	Anna	Yen
2x10	7x10
	10x7	3x7
20 u	70 u	21 u

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

710 of Min's spending = 15 of Anna's spending
710 of Min's spending =1x75x7 of Anna's spending
710 of Min's spending = 735 of Anna's spending

Min : Anna
10 : 35
2 : 7

Yen's spending in percent when compared to Anna's
= 100% - 70%
= 30%

Anna : Yen
100 : 30
10 : 3

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

Min : Anna : Yen
20 : 70 : 21

(b)

	Min	Anna	Yen
Before	20 u	70 u	21 u
Change		- 49 u
After	20 u	21 u	21 u

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

49 u = 3087

1 u = 3087 ÷ 49 = 63

Amount that Yen spent
= 21 u
= 21 x 63
= $1323 

Answer(s): (a) 20 : 70 : 21; (b) $1323