Three women, Jen, Kathy and Linda went on a shopping spree. 90% of Jen's spending was equal to ¹₆ of Kathy's spending. Linda's spending was  25% less than Kathy's. If Kathy spent $1620 less, she would spend the same amount of money as Linda.

1. Find the ratio of Jen's spending to Kathy's to Linda's.
2. How much did Linda spend?

Jen	Kathy	Linda
5x4	27x4
	4x27	3x27
20 u	108 u	81 u

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

910 of Jen's spending = 16 of Kathy's spending
910 of Jen's spending =1x96x9 of Kathy's spending
910 of Jen's spending = 954 of Kathy's spending

Jen : Kathy
10 : 54
5 : 27

Linda's spending in percent when compared to Kathy's
= 100% - 25%
= 75%

Kathy : Linda
100 : 75
4 : 3

Kathy's spending is the repeated identity.  Make Kathy's spending the same.  LCM of 27 and 4 is 108.

Jen : Kathy : Linda
20 : 108 : 81

(b)

	Jen	Kathy	Linda
Before	20 u	108 u	81 u
Change		- 27 u
After	20 u	81 u	81 u

Additional amount that Kathy would have to spend less to be the same as Linda
= 108 u - 81 u
= 27 u

27 u = 1620

1 u = 1620 ÷ 27 = 60

Amount that Linda spent
= 81 u
= 81 x 60
= $4860 

Answer(s): (a) 20 : 108 : 81; (b) $4860