Three women, Diana, Tina and Penelope went on a shopping spree. 30% of Diana's spending was equal to ¹₂ of Tina's spending. Penelope's spending was  70% less than Tina's. If Tina spent $1071 less, she would spend the same amount of money as Penelope.

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

Diana	Tina	Penelope
5x10	3x10
	10x3	3x3
50 u	30 u	9 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Diana's spending is equal to ¹₂ of Tina's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Diana's spending = 12 of Tina's spending
310 of Diana's spending =1x32x3 of Tina's spending
310 of Diana's spending = 36 of Tina's spending

Diana : Tina
10 : 6
5 : 3

Penelope's spending in percent when compared to Tina's
= 100% - 70%
= 30%

Tina : Penelope
100 : 30
10 : 3

Tina's spending is the repeated identity.  Make Tina's spending the same.  LCM of 3 and 10 is 30.

Diana : Tina : Penelope
50 : 30 : 9

(b)

	Diana	Tina	Penelope
Before	50 u	30 u	9 u
Change		- 21 u
After	50 u	9 u	9 u

Additional amount that Tina would have to spend less to be the same as Penelope
= 30 u - 9 u
= 21 u

21 u = 1071

1 u = 1071 ÷ 21 = 51

Amount that Penelope spent
= 9 u
= 9 x 51
= $459 

Answer(s): (a) 50 : 30 : 9; (b) $459