Three women, Kimberly, Kylie and Emma went on a shopping spree. 90% of Kimberly's spending was equal to ¹₆ of Kylie's spending. Emma's spending was  25% more than Kylie's. If Kylie spent another $1701, she would spend the same amount of money as Emma.

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

Kimberly	Kylie	Emma
5x4	27x4
	4x27	5x27
20 u	108 u	135 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Kimberly's spending is equal to ¹₆ of Kylie's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Kimberly's spending = 16 of Kylie's spending
910 of Kimberly's spending =1x96x9 of Kylie's spending
910 of Kimberly's spending = 954 of Kylie's spending

Kimberly : Kylie
10 : 54
5 : 27

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 27 and 4 is 108.

Kimberly : Kylie : Emma
20 : 108 : 135

(b)

	Kimberly	Kylie	Emma
Before	20 u	108 u	135 u
Change		+ 27 u
After	20 u	135 u	135 u

Additional amount that Kylie would have to spend to be the same as Emma
= 135 u - 108 u
= 27 u

27 u = 1701

1 u = 1701 ÷ 27 = 63

Amount that Kimberly spent
= 20 u
= 20 x 63
= $1260 

Answer(s): (a) 20 : 108 : 135; (b) $1260