Three women, Mary, Linda and Pamela went on a shopping spree. 30% of Mary's spending was equal to ¹₆ of Linda's spending. Pamela's spending was  25% more than Linda's. If Linda spent another $369, she would spend the same amount of money as Pamela.

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

Mary	Linda	Pamela
5x4	9x4
	4x9	5x9
20 u	36 u	45 u

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

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

Mary : Linda
10 : 18
5 : 9

Pamela's spending in percent when compared to Linda's
= 100% + 25%
= 125%

Linda : Pamela
100 : 125
4 : 5

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

Mary : Linda : Pamela
20 : 36 : 45

(b)

	Mary	Linda	Pamela
Before	20 u	36 u	45 u
Change		+ 9 u
After	20 u	45 u	45 u

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

9 u = 369

1 u = 369 ÷ 9 = 41

Amount that Mary spent
= 20 u
= 20 x 41
= $820 

Answer(s): (a) 20 : 36 : 45; (b) $820