Three women, Anna, Hilda and Shannon went on a shopping spree. 70% of Anna's spending was equal to ¹₂ of Hilda's spending. Shannon's spending was  50% more than Hilda's. If Hilda spent another $532, she would spend the same amount of money as Shannon.

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

Anna	Hilda	Shannon
5x2	7x2
	2x7	3x7
10 u	14 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Anna's spending is equal to ¹₂ of Hilda's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Anna's spending = 12 of Hilda's spending
710 of Anna's spending =1x72x7 of Hilda's spending
710 of Anna's spending = 714 of Hilda's spending

Anna : Hilda
10 : 14
5 : 7

Shannon's spending in percent when compared to Hilda's
= 100% + 50%
= 150%

Hilda : Shannon
100 : 150
2 : 3

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

Anna : Hilda : Shannon
10 : 14 : 21

(b)

	Anna	Hilda	Shannon
Before	10 u	14 u	21 u
Change		+ 7 u
After	10 u	21 u	21 u

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

7 u = 532

1 u = 532 ÷ 7 = 76

Amount that Anna spent
= 10 u
= 10 x 76
= $760 

Answer(s): (a) 10 : 14 : 21; (b) $760