Three women, Marion, Tina and Lucy went on a shopping spree. 70% of Marion's spending was equal to ¹₅ of Tina's spending. Lucy's spending was  60% more than Tina's. If Tina spent another $1680, she would spend the same amount of money as Lucy.

1. Find the ratio of Marion's spending to Tina's to Lucy's.
2. How much did Marion spend?

Marion	Tina	Lucy
2x5	7x5
	5x7	8x7
10 u	35 u	56 u

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

710 of Marion's spending = 15 of Tina's spending
710 of Marion's spending =1x75x7 of Tina's spending
710 of Marion's spending = 735 of Tina's spending

Marion : Tina
10 : 35
2 : 7

Lucy's spending in percent when compared to Tina's
= 100% + 60%
= 160%

Tina : Lucy
100 : 160
5 : 8

Tina's spending is the repeated identity.  Make Tina's spending the same.  LCM of 7 and 5 is 35.

Marion : Tina : Lucy
10 : 35 : 56

(b)

	Marion	Tina	Lucy
Before	10 u	35 u	56 u
Change		+ 21 u
After	10 u	56 u	56 u

Additional amount that Tina would have to spend to be the same as Lucy
= 56 u - 35 u
= 21 u

21 u = 1680

1 u = 1680 ÷ 21 = 80

Amount that Marion spent
= 10 u
= 10 x 80
= $800 

Answer(s): (a) 10 : 35 : 56; (b) $800