Three women, Dana, Opal and Nicole went on a shopping spree. 90% of Dana's spending was equal to ¹₂ of Opal's spending. Nicole's spending was  60% more than Opal's. If Opal spent another $621, she would spend the same amount of money as Nicole.

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

Dana	Opal	Nicole
5x5	9x5
	5x9	8x9
25 u	45 u	72 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Dana's spending is equal to ¹₂ of Opal's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Dana's spending = 12 of Opal's spending
910 of Dana's spending =1x92x9 of Opal's spending
910 of Dana's spending = 918 of Opal's spending

Dana : Opal
10 : 18
5 : 9

Nicole's spending in percent when compared to Opal's
= 100% + 60%
= 160%

Opal : Nicole
100 : 160
5 : 8

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

Dana : Opal : Nicole
25 : 45 : 72

(b)

	Dana	Opal	Nicole
Before	25 u	45 u	72 u
Change		+ 27 u
After	25 u	72 u	72 u

Additional amount that Opal would have to spend to be the same as Nicole
= 72 u - 45 u
= 27 u

27 u = 621

1 u = 621 ÷ 27 = 23

Amount that Dana spent
= 25 u
= 25 x 23
= $575 

Answer(s): (a) 25 : 45 : 72; (b) $575