Three women, Yen, Linda and Nicole went on a shopping spree. 30% of Yen's spending was equal to ¹₆ of Linda's spending. Nicole's spending was  60% more than Linda's. If Linda spent another $2565, she would spend the same amount of money as Nicole.

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

Yen	Linda	Nicole
5x5	9x5
	5x9	8x9
25 u	45 u	72 u

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

310 of Yen's spending = 16 of Linda's spending
310 of Yen's spending =1x36x3 of Linda's spending
310 of Yen's spending = 318 of Linda's spending

Yen : Linda
10 : 18
5 : 9

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

Linda : Nicole
100 : 160
5 : 8

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

Yen : Linda : Nicole
25 : 45 : 72

(b)

	Yen	Linda	Nicole
Before	25 u	45 u	72 u
Change		+ 27 u
After	25 u	72 u	72 u

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

27 u = 2565

1 u = 2565 ÷ 27 = 95

Amount that Yen spent
= 25 u
= 25 x 95
= $2375 

Answer(s): (a) 25 : 45 : 72; (b) $2375