Three women, Yoko, Emma and Jane went on a shopping spree. 70% of Yoko's spending was equal to ¹₂ of Emma's spending. Jane's spending was  25% less than Emma's. If Emma spent $455 less, she would spend the same amount of money as Jane.

1. Find the ratio of Yoko's spending to Emma's to Jane's.
2. How much did Jane spend?

Yoko	Emma	Jane
5x4	7x4
	4x7	3x7
20 u	28 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Yoko's spending is equal to ¹₂ of Emma's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Yoko's spending = 12 of Emma's spending
710 of Yoko's spending =1x72x7 of Emma's spending
710 of Yoko's spending = 714 of Emma's spending

Yoko : Emma
10 : 14
5 : 7

Jane's spending in percent when compared to Emma's
= 100% - 25%
= 75%

Emma : Jane
100 : 75
4 : 3

Emma's spending is the repeated identity.  Make Emma's spending the same.  LCM of 7 and 4 is 28.

Yoko : Emma : Jane
20 : 28 : 21

(b)

	Yoko	Emma	Jane
Before	20 u	28 u	21 u
Change		- 7 u
After	20 u	21 u	21 u

Additional amount that Emma would have to spend less to be the same as Jane
= 28 u - 21 u
= 7 u

7 u = 455

1 u = 455 ÷ 7 = 65

Amount that Jane spent
= 21 u
= 21 x 65
= $1365 

Answer(s): (a) 20 : 28 : 21; (b) $1365