Three women, Natalie, Wendy and Esther went on a shopping spree. 30% of Natalie's spending was equal to ¹₆ of Wendy's spending. Esther's spending was  40% more than Wendy's. If Wendy spent another $1566, she would spend the same amount of money as Esther.

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

Natalie	Wendy	Esther
5x5	9x5
	5x9	7x9
25 u	45 u	63 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Natalie's spending is equal to ¹₆ of Wendy's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Natalie's spending = 16 of Wendy's spending
310 of Natalie's spending =1x36x3 of Wendy's spending
310 of Natalie's spending = 318 of Wendy's spending

Natalie : Wendy
10 : 18
5 : 9

Esther's spending in percent when compared to Wendy's
= 100% + 40%
= 140%

Wendy : Esther
100 : 140
5 : 7

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

Natalie : Wendy : Esther
25 : 45 : 63

(b)

	Natalie	Wendy	Esther
Before	25 u	45 u	63 u
Change		+ 18 u
After	25 u	63 u	63 u

Additional amount that Wendy would have to spend to be the same as Esther
= 63 u - 45 u
= 18 u

18 u = 1566

1 u = 1566 ÷ 18 = 87

Amount that Natalie spent
= 25 u
= 25 x 87
= $2175 

Answer(s): (a) 25 : 45 : 63; (b) $2175