Three women, Gillian, Sarah and Victoria went on a shopping spree. 70% of Gillian's spending was equal to ¹₅ of Sarah's spending. Victoria's spending was  70% less than Sarah's. If Sarah spent $5880 less, she would spend the same amount of money as Victoria.

1. Find the ratio of Gillian's spending to Sarah's to Victoria's.
2. How much did Victoria spend?

Gillian	Sarah	Victoria
2x10	7x10
	10x7	3x7
20 u	70 u	21 u

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

710 of Gillian's spending = 15 of Sarah's spending
710 of Gillian's spending =1x75x7 of Sarah's spending
710 of Gillian's spending = 735 of Sarah's spending

Gillian : Sarah
10 : 35
2 : 7

Victoria's spending in percent when compared to Sarah's
= 100% - 70%
= 30%

Sarah : Victoria
100 : 30
10 : 3

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

Gillian : Sarah : Victoria
20 : 70 : 21

(b)

	Gillian	Sarah	Victoria
Before	20 u	70 u	21 u
Change		- 49 u
After	20 u	21 u	21 u

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

49 u = 5880

1 u = 5880 ÷ 49 = 120

Amount that Victoria spent
= 21 u
= 21 x 120
= $2520 

Answer(s): (a) 20 : 70 : 21; (b) $2520