Three women, Nicole, Irene and Hilda went on a shopping spree. 30% of Nicole's spending was equal to ¹₂ of Irene's spending. Hilda's spending was  60% less than Irene's. If Irene spent $702 less, she would spend the same amount of money as Hilda.

1. Find the ratio of Nicole's spending to Irene's to Hilda's.
2. How much did Hilda spend?

Nicole	Irene	Hilda
5x5	3x5
	5x3	2x3
25 u	15 u	6 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Nicole's spending is equal to ¹₂ of Irene's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Nicole's spending = 12 of Irene's spending
310 of Nicole's spending =1x32x3 of Irene's spending
310 of Nicole's spending = 36 of Irene's spending

Nicole : Irene
10 : 6
5 : 3

Hilda's spending in percent when compared to Irene's
= 100% - 60%
= 40%

Irene : Hilda
100 : 40
5 : 2

Irene's spending is the repeated identity.  Make Irene's spending the same.  LCM of 3 and 5 is 15.

Nicole : Irene : Hilda
25 : 15 : 6

(b)

	Nicole	Irene	Hilda
Before	25 u	15 u	6 u
Change		- 9 u
After	25 u	6 u	6 u

Additional amount that Irene would have to spend less to be the same as Hilda
= 15 u - 6 u
= 9 u

9 u = 702

1 u = 702 ÷ 9 = 78

Amount that Hilda spent
= 6 u
= 6 x 78
= $468 

Answer(s): (a) 25 : 15 : 6; (b) $468