Three women, Betty, Anna and Risa went on a shopping spree. 70% of Betty's spending was equal to ¹₅ of Anna's spending. Risa's spending was  50% more than Anna's. If Anna spent another $462, she would spend the same amount of money as Risa.

1. Find the ratio of Betty's spending to Anna's to Risa's.
2. How much did Betty spend?

Betty	Anna	Risa
2x2	7x2
	2x7	3x7
4 u	14 u	21 u

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

710 of Betty's spending = 15 of Anna's spending
710 of Betty's spending =1x75x7 of Anna's spending
710 of Betty's spending = 735 of Anna's spending

Betty : Anna
10 : 35
2 : 7

Risa's spending in percent when compared to Anna's
= 100% + 50%
= 150%

Anna : Risa
100 : 150
2 : 3

Anna's spending is the repeated identity.  Make Anna's spending the same.  LCM of 7 and 2 is 14.

Betty : Anna : Risa
4 : 14 : 21

(b)

	Betty	Anna	Risa
Before	4 u	14 u	21 u
Change		+ 7 u
After	4 u	21 u	21 u

Additional amount that Anna would have to spend to be the same as Risa
= 21 u - 14 u
= 7 u

7 u = 462

1 u = 462 ÷ 7 = 66

Amount that Betty spent
= 4 u
= 4 x 66
= $264 

Answer(s): (a) 4 : 14 : 21; (b) $264