Three women, Pamela, Cathy and Emma went on a shopping spree. 90% of Pamela's spending was equal to ¹₅ of Cathy's spending. Emma's spending was  80% less than Cathy's. If Cathy spent $1872 less, she would spend the same amount of money as Emma.

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

Pamela	Cathy	Emma
2x5	9x5
	5x9	1x9
10 u	45 u	9 u

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

910 of Pamela's spending = 15 of Cathy's spending
910 of Pamela's spending =1x95x9 of Cathy's spending
910 of Pamela's spending = 945 of Cathy's spending

Pamela : Cathy
10 : 45
2 : 9

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

Cathy : Emma
100 : 20
5 : 1

Cathy's spending is the repeated identity.  Make Cathy's spending the same.  LCM of 9 and 5 is 45.

Pamela : Cathy : Emma
10 : 45 : 9

(b)

	Pamela	Cathy	Emma
Before	10 u	45 u	9 u
Change		- 36 u
After	10 u	9 u	9 u

Additional amount that Cathy would have to spend less to be the same as Emma
= 45 u - 9 u
= 36 u

36 u = 1872

1 u = 1872 ÷ 36 = 52

Amount that Emma spent
= 9 u
= 9 x 52
= $468 

Answer(s): (a) 10 : 45 : 9; (b) $468