Three women, Penelope, Tina and Tiffany went on a shopping spree. 70% of Penelope's spending was equal to ¹₆ of Tina's spending. Tiffany's spending was  50% more than Tina's. If Tina spent another $1869, she would spend the same amount of money as Tiffany.

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

Penelope	Tina	Tiffany
5x2	21x2
	2x21	3x21
10 u	42 u	63 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Penelope's spending is equal to ¹₆ of Tina's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Penelope's spending = 16 of Tina's spending
710 of Penelope's spending =1x76x7 of Tina's spending
710 of Penelope's spending = 742 of Tina's spending

Penelope : Tina
10 : 42
5 : 21

Tiffany's spending in percent when compared to Tina's
= 100% + 50%
= 150%

Tina : Tiffany
100 : 150
2 : 3

Tina's spending is the repeated identity.  Make Tina's spending the same.  LCM of 21 and 2 is 42.

Penelope : Tina : Tiffany
10 : 42 : 63

(b)

	Penelope	Tina	Tiffany
Before	10 u	42 u	63 u
Change		+ 21 u
After	10 u	63 u	63 u

Additional amount that Tina would have to spend to be the same as Tiffany
= 63 u - 42 u
= 21 u

21 u = 1869

1 u = 1869 ÷ 21 = 89

Amount that Penelope spent
= 10 u
= 10 x 89
= $890 

Answer(s): (a) 10 : 42 : 63; (b) $890