Three women, Hazel, Usha and Betty went on a shopping spree. 70% of Hazel's spending was equal to ¹₅ of Usha's spending. Betty's spending was  80% less than Usha's. If Usha spent $3248 less, she would spend the same amount of money as Betty.

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

Hazel	Usha	Betty
2x5	7x5
	5x7	1x7
10 u	35 u	7 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Hazel's spending is equal to ¹₅ of Usha's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Hazel's spending = 15 of Usha's spending
710 of Hazel's spending =1x75x7 of Usha's spending
710 of Hazel's spending = 735 of Usha's spending

Hazel : Usha
10 : 35
2 : 7

Betty's spending in percent when compared to Usha's
= 100% - 80%
= 20%

Usha : Betty
100 : 20
5 : 1

Usha's spending is the repeated identity.  Make Usha's spending the same.  LCM of 7 and 5 is 35.

Hazel : Usha : Betty
10 : 35 : 7

(b)

	Hazel	Usha	Betty
Before	10 u	35 u	7 u
Change		- 28 u
After	10 u	7 u	7 u

Additional amount that Usha would have to spend less to be the same as Betty
= 35 u - 7 u
= 28 u

28 u = 3248

1 u = 3248 ÷ 28 = 116

Amount that Betty spent
= 7 u
= 7 x 116
= $812 

Answer(s): (a) 10 : 35 : 7; (b) $812