Three women, Sarah, Tammy and Opal went on a shopping spree. 30% of Sarah's spending was equal to ¹₆ of Tammy's spending. Opal's spending was  25% more than Tammy's. If Tammy spent another $612, she would spend the same amount of money as Opal.

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

Sarah	Tammy	Opal
5x4	9x4
	4x9	5x9
20 u	36 u	45 u

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

310 of Sarah's spending = 16 of Tammy's spending
310 of Sarah's spending =1x36x3 of Tammy's spending
310 of Sarah's spending = 318 of Tammy's spending

Sarah : Tammy
10 : 18
5 : 9

Opal's spending in percent when compared to Tammy's
= 100% + 25%
= 125%

Tammy : Opal
100 : 125
4 : 5

Tammy's spending is the repeated identity.  Make Tammy's spending the same.  LCM of 9 and 4 is 36.

Sarah : Tammy : Opal
20 : 36 : 45

(b)

	Sarah	Tammy	Opal
Before	20 u	36 u	45 u
Change		+ 9 u
After	20 u	45 u	45 u

Additional amount that Tammy would have to spend to be the same as Opal
= 45 u - 36 u
= 9 u

9 u = 612

1 u = 612 ÷ 9 = 68

Amount that Sarah spent
= 20 u
= 20 x 68
= $1360 

Answer(s): (a) 20 : 36 : 45; (b) $1360