Three women, Usha, Abi and Lynn went on a shopping spree. 70% of Usha's spending was equal to ¹₂ of Abi's spending. Lynn's spending was  40% less than Abi's. If Abi spent $980 less, she would spend the same amount of money as Lynn.

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

Usha	Abi	Lynn
5x5	7x5
	5x7	3x7
25 u	35 u	21 u

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

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

Usha : Abi
10 : 14
5 : 7

Lynn's spending in percent when compared to Abi's
= 100% - 40%
= 60%

Abi : Lynn
100 : 60
5 : 3

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

Usha : Abi : Lynn
25 : 35 : 21

(b)

	Usha	Abi	Lynn
Before	25 u	35 u	21 u
Change		- 14 u
After	25 u	21 u	21 u

Additional amount that Abi would have to spend less to be the same as Lynn
= 35 u - 21 u
= 14 u

14 u = 980

1 u = 980 ÷ 14 = 70

Amount that Lynn spent
= 21 u
= 21 x 70
= $1470 

Answer(s): (a) 25 : 35 : 21; (b) $1470