Three women, Fiona, Betty and Nora went on a shopping spree. 90% of Fiona's spending was equal to ¹₆ of Betty's spending. Nora's spending was  80% less than Betty's. If Betty spent $6804 less, she would spend the same amount of money as Nora.

1. Find the ratio of Fiona's spending to Betty's to Nora's.
2. How much did Nora spend?

Fiona	Betty	Nora
5x5	27x5
	5x27	1x27
25 u	135 u	27 u

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

910 of Fiona's spending = 16 of Betty's spending
910 of Fiona's spending =1x96x9 of Betty's spending
910 of Fiona's spending = 954 of Betty's spending

Fiona : Betty
10 : 54
5 : 27

Nora's spending in percent when compared to Betty's
= 100% - 80%
= 20%

Betty : Nora
100 : 20
5 : 1

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

Fiona : Betty : Nora
25 : 135 : 27

(b)

	Fiona	Betty	Nora
Before	25 u	135 u	27 u
Change		- 108 u
After	25 u	27 u	27 u

Additional amount that Betty would have to spend less to be the same as Nora
= 135 u - 27 u
= 108 u

108 u = 6804

1 u = 6804 ÷ 108 = 63

Amount that Nora spent
= 27 u
= 27 x 63
= $1701 

Answer(s): (a) 25 : 135 : 27; (b) $1701