Three women, Tiffany, Diana and Sarah went on a shopping spree. 90% of Tiffany's spending was equal to ¹₆ of Diana's spending. Sarah's spending was  40% less than Diana's. If Diana spent $1674 less, she would spend the same amount of money as Sarah.

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

Tiffany	Diana	Sarah
5x5	27x5
	5x27	3x27
25 u	135 u	81 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Tiffany's spending is equal to ¹₆ of Diana's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Tiffany's spending = 16 of Diana's spending
910 of Tiffany's spending =1x96x9 of Diana's spending
910 of Tiffany's spending = 954 of Diana's spending

Tiffany : Diana
10 : 54
5 : 27

Sarah's spending in percent when compared to Diana's
= 100% - 40%
= 60%

Diana : Sarah
100 : 60
5 : 3

Diana's spending is the repeated identity.  Make Diana's spending the same.  LCM of 27 and 5 is 135.

Tiffany : Diana : Sarah
25 : 135 : 81

(b)

	Tiffany	Diana	Sarah
Before	25 u	135 u	81 u
Change		- 54 u
After	25 u	81 u	81 u

Additional amount that Diana would have to spend less to be the same as Sarah
= 135 u - 81 u
= 54 u

54 u = 1674

1 u = 1674 ÷ 54 = 31

Amount that Sarah spent
= 81 u
= 81 x 31
= $2511 

Answer(s): (a) 25 : 135 : 81; (b) $2511