Three women, Natalie, Pamela and Lucy went on a shopping spree. 70% of Natalie's spending was equal to ¹₅ of Pamela's spending. Lucy's spending was  60% more than Pamela's. If Pamela spent another $1092, she would spend the same amount of money as Lucy.

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

Natalie	Pamela	Lucy
2x5	7x5
	5x7	8x7
10 u	35 u	56 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Natalie's spending is equal to ¹₅ of Pamela's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Natalie's spending = 15 of Pamela's spending
710 of Natalie's spending =1x75x7 of Pamela's spending
710 of Natalie's spending = 735 of Pamela's spending

Natalie : Pamela
10 : 35
2 : 7

Lucy's spending in percent when compared to Pamela's
= 100% + 60%
= 160%

Pamela : Lucy
100 : 160
5 : 8

Pamela's spending is the repeated identity.  Make Pamela's spending the same.  LCM of 7 and 5 is 35.

Natalie : Pamela : Lucy
10 : 35 : 56

(b)

	Natalie	Pamela	Lucy
Before	10 u	35 u	56 u
Change		+ 21 u
After	10 u	56 u	56 u

Additional amount that Pamela would have to spend to be the same as Lucy
= 56 u - 35 u
= 21 u

21 u = 1092

1 u = 1092 ÷ 21 = 52

Amount that Natalie spent
= 10 u
= 10 x 52
= $520 

Answer(s): (a) 10 : 35 : 56; (b) $520