Three women, Usha, Kylie and Emma went on a shopping spree. 70% of Usha's spending was equal to ¹₂ of Kylie's spending. Emma's spending was  25% more than Kylie's. If Kylie spent another $588, she would spend the same amount of money as Emma.

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

Usha	Kylie	Emma
5x4	7x4
	4x7	5x7
20 u	28 u	35 u

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

710 of Usha's spending = 12 of Kylie's spending
710 of Usha's spending =1x72x7 of Kylie's spending
710 of Usha's spending = 714 of Kylie's spending

Usha : Kylie
10 : 14
5 : 7

Emma's spending in percent when compared to Kylie's
= 100% + 25%
= 125%

Kylie : Emma
100 : 125
4 : 5

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

Usha : Kylie : Emma
20 : 28 : 35

(b)

	Usha	Kylie	Emma
Before	20 u	28 u	35 u
Change		+ 7 u
After	20 u	35 u	35 u

Additional amount that Kylie would have to spend to be the same as Emma
= 35 u - 28 u
= 7 u

7 u = 588

1 u = 588 ÷ 7 = 84

Amount that Usha spent
= 20 u
= 20 x 84
= $1680 

Answer(s): (a) 20 : 28 : 35; (b) $1680