Three women, Jane, Abi and Sarah went on a shopping spree. 90% of Jane's spending was equal to ¹₅ of Abi's spending. Sarah's spending was  70% less than Abi's. If Abi spent $6426 less, she would spend the same amount of money as Sarah.

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

Jane	Abi	Sarah
2x10	9x10
	10x9	3x9
20 u	90 u	27 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Jane's spending is equal to ¹₅ of Abi's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Jane's spending = 15 of Abi's spending
910 of Jane's spending =1x95x9 of Abi's spending
910 of Jane's spending = 945 of Abi's spending

Jane : Abi
10 : 45
2 : 9

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

Abi : Sarah
100 : 30
10 : 3

Abi's spending is the repeated identity.  Make Abi's spending the same.  LCM of 9 and 10 is 90.

Jane : Abi : Sarah
20 : 90 : 27

(b)

	Jane	Abi	Sarah
Before	20 u	90 u	27 u
Change		- 63 u
After	20 u	27 u	27 u

Additional amount that Abi would have to spend less to be the same as Sarah
= 90 u - 27 u
= 63 u

63 u = 6426

1 u = 6426 ÷ 63 = 102

Amount that Sarah spent
= 27 u
= 27 x 102
= $2754 

Answer(s): (a) 20 : 90 : 27; (b) $2754