Three women, Min, Esther and Cathy went on a shopping spree. 70% of Min's spending was equal to ¹₂ of Esther's spending. Cathy's spending was  80% less than Esther's. If Esther spent $2520 less, she would spend the same amount of money as Cathy.

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

Min	Esther	Cathy
5x5	7x5
	5x7	1x7
25 u	35 u	7 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Min's spending is equal to ¹₂ of Esther's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Min's spending = 12 of Esther's spending
710 of Min's spending =1x72x7 of Esther's spending
710 of Min's spending = 714 of Esther's spending

Min : Esther
10 : 14
5 : 7

Cathy's spending in percent when compared to Esther's
= 100% - 80%
= 20%

Esther : Cathy
100 : 20
5 : 1

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

Min : Esther : Cathy
25 : 35 : 7

(b)

	Min	Esther	Cathy
Before	25 u	35 u	7 u
Change		- 28 u
After	25 u	7 u	7 u

Additional amount that Esther would have to spend less to be the same as Cathy
= 35 u - 7 u
= 28 u

28 u = 2520

1 u = 2520 ÷ 28 = 90

Amount that Cathy spent
= 7 u
= 7 x 90
= $630 

Answer(s): (a) 25 : 35 : 7; (b) $630