Three women, Hilda, Yoko and Diana went on a shopping spree. 70% of Hilda's spending was equal to ¹₅ of Yoko's spending. Diana's spending was  40% more than Yoko's. If Yoko spent another $1358, she would spend the same amount of money as Diana.

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

Hilda	Yoko	Diana
2x5	7x5
	5x7	7x7
10 u	35 u	49 u

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

710 of Hilda's spending = 15 of Yoko's spending
710 of Hilda's spending =1x75x7 of Yoko's spending
710 of Hilda's spending = 735 of Yoko's spending

Hilda : Yoko
10 : 35
2 : 7

Diana's spending in percent when compared to Yoko's
= 100% + 40%
= 140%

Yoko : Diana
100 : 140
5 : 7

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

Hilda : Yoko : Diana
10 : 35 : 49

(b)

	Hilda	Yoko	Diana
Before	10 u	35 u	49 u
Change		+ 14 u
After	10 u	49 u	49 u

Additional amount that Yoko would have to spend to be the same as Diana
= 49 u - 35 u
= 14 u

14 u = 1358

1 u = 1358 ÷ 14 = 97

Amount that Hilda spent
= 10 u
= 10 x 97
= $970 

Answer(s): (a) 10 : 35 : 49; (b) $970